## Electricity and Magnetism

Each of the following questions comprises two statements. The assertion is expressed by Statement 1 and the reason is expressed by Statement 2.

Each question has four options (1), (2), (3), and (4) as given below, out of which only ONE is correct.

- Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.
- Statement 1 is true; Statement 2 is true; but Statement 2 is not a correct explanation of Statement 1.
- Statement 1 is true and Statement 2 is false.
- Statement 1 is false and Statement 2 is true.
- Both Statement 1 and Statement 2 are false.

Some questions are preceded, by a supporting paragraph in addition to the statements.

## Current Electricity

**Question 1. Statement 1** The total current entering and appointing the circuit is equal to the total current leaving the circuit, according to Kirchhoff’s law.

**Statement 2** It is based on the law of conservation of energy.

**Answer:** 3. Statement 1 is true and Statement 2 is false.

Since the charge does not accumulate at any point, the total incoming current is equal to the total outgoing current. This corresponds to the conservation of charge and not of energy.

**Question 2. Statement 1** A current continues to flow through a superconducting coil even after its supply is switched off.

**Statement 2** Superconducting coils show the Meissner effect.

**Answer:** 2. Statement 1 is true; Statement 2 is true; but Statement 2 is not a correct explanation of Statement 1.

The Meissner effect is the expulsion of the magnetic field from a superconductor during its transition to the superconducting when cooled below the transition temperature Tc (usually close to absolute zero). Due to its zero resistance to the current flow, current continues to flow when switched off.

**Question 3. Statement 1** An electric bulb glows instantly as it is switched on.

**Statement 2** The drift speed of electrons in a metallic wire is very large.

**Answer:** 3. Statement 1 is true and Statement 2 is false.

A conductor is full of free electrons. Any disturbance anywhere is instantly transmitted to the bulb which glows. The drift speed is small due to the collisions between the electrons and the ions.

**Question 4. Statement 1** Ohm’s law is applicable to all conducting elements.

**Statement 2** Ohm’s law is a fundamental law.

**Answer:** 5. Both Statement 1 and Statement 2 are false.

Ohm’s law is valid for circuits with a constant resistance, for which the V-I graph is a straight line with a positive slope. It is not valid for semiconductors, diodes, and superconductors. Ohm’s law is not a universal (fundamental) law but an empirical law.

**Question 5. Statement 1** It is advantageous to transmit electric power at a high voltage.

**Statement 2** A high voltage implies a high current.

**Answer:** 3. Statement 1 is true and Statement 2 is false.

In an AC circuit, the voltage is stepped up by a transformer. At a high voltage, the current is reduced, so the power loss is reduced.

**Question 6. Statement 1** Current is passed through a metallic wire so that it becomes red hot. When cold water is poured on one half of its portion, the other half becomes hotter.

**Statement 2** Resistance decreases due to a decrease in temperature.

**Answer:** 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.

When cold water is poured on one half of the red-hot conductor, its temperature is reduced, resistance is reduced and the current through it is increased so that the other half becomes hotter.

**Question 7. Statement 1** In the given circuit, the emf is 2 V and the internal resistance of the cell is 1 Ω. When R = 1Ω, the reading of the voltmeter is 1 V.

**Statement 2** V= ε -IR, where ε = 2 V.

Hence, \(I=\frac{2 \mathrm{~V}}{2 \Omega}=1 \mathrm{~A}\)

**Answer:** 3. Statement 1 is true and Statement 2 is false.

The voltmeter reading gives the terminal voltage across the cell, so V= ε -Ir (and not ε-IR).

Main current = \(I=\frac{\varepsilon}{R+r}=\frac{2 \mathrm{~V}}{2 \Omega}=1 \mathrm{~A}\)

V = 2 V-(1A)(1Ω)=1V

**Question 8. Statement 1** In a simple battery circuit, the point of the lowest potential is the positive terminal of the battery.

**Statement 2** Current flows towards the point of the higher potential, as it does such a circuit from the negative to the positive terminal.

**Answer:** 5. Both Statement 1 and Statement 2 are false.

The point of lowest potential of the circuit is the negative terminal of the cell. Current flows from the higher potential (positive terminal) to the negative terminal (lower potential) through the outer circuit.

**Question 9. Statement 1** The conductivity of an electrolyte is very low as compared to a metal at room temperature.

**Statement 2** The number density of free ions in an electrolyte is much smaller as compared to the number density of free electrons in metals. Further, ions, being heavier, drift much more slowly.

**Answer:** 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.

Conduction in an electrolyte is due to the movement of free ions which are comparatively much heavier than electrons and have a smaller drift speed. Hence, metals have higher conductivity than electrolytes.

**Question 10. Statement 1** A domestic electrical appliance working on a threepin plug will continue working even if the top pin is removed.

**Statement 2** The top pin (earth) is only a safety measure.

**Answer:** 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.

The top pin is used for earthling as a safety measure. The remaining two terminals are active (live) and neutral which supply power to a device.

**Question 11. Statement 1** Electronic appliances with metallic bodies, for example, heaters and electric irons, have three-pin connections, whereas an electric bulb has a two-pin connection.

**Statement 2** Three-pin connections reduce the heating of connecting cables.

**Answer:** 3. Statement 1 is true and Statement 2 is false.

Devices with metallic bodies are connected to the ground (top pin) as a safety measure. No grounding is required for bulbs.

**Question 12. Statement 1** Good conductors of heat are also good conductors of electricity, and vice versa.

**Statement 2** Mainlyelectrons are responsible for these connections.

**Answer:** 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.

Conduction of heat and current electricity are both linked to the motion of free electrons. According to Wiedemann-Franz law, the ratio of the electronic contribution to thermal conductivity (K) to the electrical conductivity (σ) of a metal is proportional to the temperature (T). This explains that good thermal conductors are also good conductors of electricity.

**Question 13. Statement 1** A larger dry cell has a higher emf.

**Statement 2** The emf of a dry cell is proportional to its size.

**Answer:** 5. Both Statement 1 and Statement 2 are false.

The large plate area of cells is responsible for its capacity (in ampere-hour) and not the emf.

**Question 14. Statement 1** A bird perches on a high-power line and nothing happens to the bird.

**Statement 2** The level of the bird is very high from the ground. So, it is not grounded through any conducting device.

**Answer:** 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.

Electricity flows through the path of least resistance. Birds do not get an electrical shock while sitting on live electrical wires because they are not good conductors of electricity. Further, the two points of contact are at the same potential and do not form a closed circuit for current to flow through the bird sitting on a power line.

## Magnetic Effect of Current

**Question 1. Statement 1** A voltmeter is connected in parallel with a circuit.

**Statement 2** The resistance of a voltmeter is very high.

**Answer:** 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.

A voltmeter is connected in parallel to measure the potential difference between two points. It has high resistance, so it draws a small current and does not change the main current appreciably.

**Question 2. Statement 1** A charge, whether stationary or in motion, produces a magnetic field around it.

**Statement 2** Moving charges produce only an electric field in the surrounding space.

**Answer:** 5. Both Statement 1 and Statement 2 are false.

A moving charge \(\left(d q v=\frac{d q}{d t} d l=I d l\right)\) is equivalent to a current element that produces a magnetic field. A charge at rest can produce an electric field.

**Question 3. Statement 1** A planar circular loop of area A and carrying current I is equivalent to a magnetic dipole of dipole moment m = IA.

**Statement 2** At large distances, the magnetic field due to a current-carrying circular loop and that due to a magnetic dipole are the same.

**Answer:** 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.

A ‘current-carrying loop is equivalent to a magnetic dipole whose dipole moment \(|\vec{m}|\) is IA ampere metre^{2}.

The magnetic field at a large distance from a circular current loop is

⇒ \(B=\frac{\mu_0 I R^2}{2\left(R^2+r^2\right)^{3 / 2}}=\frac{\mu_0 I R^2}{2 r^3} \quad(\text { for } r \gg R)\)

∴ \(\frac{\mu_0 I \pi R^2}{2 \pi r^3}=\frac{\mu_0}{2 \pi} \frac{I A}{r^3}=\frac{\mu_0 m}{2 \pi r^3}\)

Where m = IA = magnetic dipole moment.

**Question 4. Statement 1** When the radius of a current-carrying loop is doubled, its magnetic moment becomes four times.

**Statement 2** The magnetic moment depends on the area of the loop.

**Answer:** 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.

The magnetic dipole moment is m =IπR^{2}.

When R is doubled, m’ = Iπ(2R)^{2} = 4 m.

This is because m ∝ area of the loop.

**Question 5. Statement 1** A charged particle can be accelerated in a cyclotron by the alternate variation of the electric field.

**Statement 2** The energy of a charged particle is increased by the electric field applied.

**Answer:** 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.

In a cyclotron,both \(\vec{E}\) and \(\vec{B}\) fields act together. The \(\vec{B}\) field provides the circular path while the \(\vec{E}\) field gives an impulse in between the gaps.

**Question 6. Statement 1** A cyclotron does not accelerate electrons.

**Statement 2** The mass of an electron is very small.

**Answer:** 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.

The frequency of the alternating electric field is kept constant, given by \(f=\frac{q B}{2 \pi m}\).

The electron mass is small and it changes considerably with speed given by \(m=\frac{m_0}{\sqrt{1-\frac{v^2}{c^2}}}\), so f is not synchronized for acceleration.

**Question 7. Statement 1** A spark occurs between the poles of a switch when the switch is opened.

**Statement 2** Current flowing in a conductor produces a magnetic field.

**Answer:** 2. Statement 1 is true; Statement 2 is true; but Statement 2 is not a correct explanation of Statement 1.

When the switch is opened, the magnetic energy stored in the coil or any inductive component gets discharged. This causes a huge current through the two terminals of the switch. This voltage across the terminal gap of the switch exceeds the dielectric strength of air and produces a spark.

**Question 8. Statement 1** If a proton and an α-particle enter a uniform magnetic field perpendicularly with the same speed, the time period of revolution of the α-particle is double that of the proton.

**Statement 2** In a magnetic field, the period of revolution of a charged particle is directly proportional to the mass of the particle and is inversely proportional to the charge of the particle.

**Answer:** 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.

The frequency of revolution of a charged particle in a magnetic field is

⇒ \(f=\frac{1}{T}=\frac{q B}{2 \pi m} \Rightarrow T=\frac{2 \pi m}{q B}\)

∴ \(T_{\text {proton }}=\frac{2 \pi m_{\text {proton }}}{q B} \text { and } T_\alpha=\frac{2 \pi \cdot 4 m_{\text {proton }}}{2 q B}=2 T_{\text {proton }}\)

Time of revolution \(\propto \frac{m}{q}\)

**Question 9. Statement 1** The energy of a charged particle moving in a uniform magnetic field does not change.

**Statement 2** The work done by the magnetic field on the charge is zero.

**Answer:** 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.

Force on a charged particle moving in a magnetic field = \(\vec{F}=q \vec{v} \times \vec{B}\) This force only provides centripetal force for circular motion and does no work. Hence, work done is zero and KE remains constant.

**Question 10. Statement 1** When a magnetic dipole is placed in a nonuniform magnetic field, only a torque acts on the dipole.

**Statement 2** A force would act on a dipole if the magnetic field is uniform.

**Answer:** 5. Both Statement 1 and Statement 2 are false.

In a nonuniform magnetic field, the two poles experience unequal forces as well as a torque. Hence, the torque and the net force act together producing translational and rotational motions.

**Question 11. Statement 1** Magnetic field lines form a closed loop in nature.

**Statement 2** Monomagnetic poles do not exist in nature.

**Answer:** 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.

Magnetic field lines always form a closed loop in nature because no magnetic monopole exists in nature. Inside the magnet they travel from the south pole to the north pole and outside, from the north pole to the south pole, thereby forming a closed loop.

## Electromagnetic Induction

**Question 1. Statement 1** The possibility of an electric bulb fusing is higher at the time of switching on and off.

**Statement 2** Inductive effects produce a surge in switching off and switching on.

**Answer:** 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.

During switching on or off a sudden change in magnetic flux induces high voltage \(\left(|e|=\frac{d \phi}{d t}\right)\) which may cause an electric bulb to fuse.

**Question 2. Statement 1** Only a change in magnetic flux will maintain the induced current in the coil.

**Statement 2** The presence of a large magnetic flux through a coil maintains a current in the coil if the circuit is continuous.

**Answer:** 3. Statement 1 is true and Statement 2 is false.

When the magnetic flux linked with a coil changes with time, the induced current is maintained. The presence of a steady magnetic flux will not induce current in a closed coil.

**Question 3. Statement 1** An emf ε is induced in a closed loop where magnetic flux is varied. The induced electric field \(\vec{E}\) is not a conservative field.

**Statement 2** The line integral \(\int \vec{E} \cdot \overrightarrow{d l}\) around a closed loop is nonzero.

**Answer:** 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.

Induced electric fields form closed loops, so that a charge moving along the loop under the induced field will experience a force parallel to its displacement, and nonzero work is done, unlike conservative forces, where the work done in a closed loop is zero. The non – conservative nature of the induced electric field is also expressed mathematically as \(\oint \vec{E} \cdot \overrightarrow{d l} \neq 0\)

**Question 4. Statement 1** If the current is flowing through a machine of iron, eddy currents are induced.

**Statement 2** The change in magnetic flux through an area causes eddy currents.

**Answer:** 5. Both Statement 1 and Statement 2 are false.

Eddy currents are induced by the time-varying magnetic flux linked with a conductor and not by the current flowing through the conductor itself.

**Question 5. Statement 1** In a moving train, a small potential difference arises across the axles of the wheels due to the earth’s magnetic field. This potential difference vanishes at the equator.

**Statement 2** At the equator, the earth’s magnetic field is horizontal.

**Answer:** 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.

A motional emf ε = Blv is produced when the moving conductor cuts the magnetic field lines. At the equator, the axles do not cut the field lines.

**Question 6. Statement 1** When a charged particle enters a magnetic field from outside, it cannot complete one rotation inside the field.

**Statement 2** The entry and exit of a charged particle into and out of a uniform magnetic field are symmetrical.

**Answer:** 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.

The charged particle that enters the magnetic field at P will experience a force \(\vec{F}=q(\vec{v} \times \vec{B})\). This force, perpendicular to \(\vec{v}\) and \(\vec{B}\), provides a centripetal force. The path followed is a semicircle. The entry and exit at P and Q are symmetrical about the center O.

image

## Electromagnetic Induction

**Question 1. Statement 1** The possibility of an electric bulb fusing is higher at the time of switching on and off.

**Statement 2** Inductive effects produce a surge in switching off and switching on.

**Answer:** 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.

During switching on or off a sudden change in magnetic flux induces high voltage \(\left(|e|=\frac{d \phi}{d t}\right)\) which may cause an electric bulb to fuse.

**Question 2. Statement 1** Only a change in magnetic flux will maintain the induced current in the coil.

**Statement 2** The presence of a large magnetic flux through a coil maintains a current in the coil if the circuit is continuous.

**Answer:** 3. Statement 1 is true and Statement 2 is false.

When the magnetic flux linked with a coil changes with time, the induced current is maintained. The presence of a steady magnetic flux will not induce current in a closed coil.

**Question 3. Statement 1** An emf 8 is induced in a closed loop where magnetic flux is varied. The induced electric field \(\vec{E}\) is not a conservative field.

**Statement 2** The line integral \(\int \vec{E} \cdot \overrightarrow{d l}\) around a closed loop is nonzero.

**Answer:** 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.

Induced electric fields form closed loops, so that a charge moving along the loop under the induced field will experience a force parallel to its displacement, and nonzero work is done, unlike conservative forces, where the work done in a closed loop is zero. The non – conservative nature of the induced electric field is also expressed mathematically as \(\oint \vec{E} \cdot \overrightarrow{d l} \neq 0\)

**Question 4. Statement 1** If the current is flowing through a machine of iron, eddy currents are induced.

**Statement 2** The change in magnetic flux through an area causes eddy currents.

**Answer:** 5. Both Statement 1 and Statement 2 are false.

Eddy currents are induced by the time-varying magnetic flux linked with a conductor and not by the current flowing through the conductor itself.

**Question 5. Statement 1** In a moving train, a small potential difference arises across the axles of the wheels due to the earth’s magnetic field. This potential difference vanishes at the equator.

**Statement 2** At the equator, the magnetic field is horizontal.

**Answer:** 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.

A motional emf ε = Blv is produced when the moving conductor cuts the magnetic field lines. At the equator, the axles do not cut the field lines.

**Question 6. Statement 1** When a charged particle enters a magnetic field from outside, it cannot complete one rotation inside the field.

**Statement 2** The entry and exit of a charged particle into and out of a uniform magnetic field are symmetrical.

**Answer:** 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.

The charged particle that enters the magnetic field at P will experience a force \(\vec{F}=q(\vec{v} \times \vec{B})\). This force, perpendicular to \(\vec{v}\) and \(\vec{B}\), provides a centripetal force. The path followed is a semicircle. The entry and exit at P and Q are symmetrical about the center O.

## Alternating Current

**Question 1. Statement 1** Faraday’s laws are consequences of the conservation of energy.

**Statement 2** In a purely resistive AC circuit the current lags behind the voltage.

**Answer:** 3. Statement 1 is true and Statement 2 is false.

Faraday’s laws of EMI follow the principle of conservation of energy. In pure resistance in an AC circuit, current and voltage are always in the same phase.

**Question 2. Statement 1** While flowing through an inductor, an alternating current lags behind the voltage by a phase angle of \(\frac{\pi}{2}\), when AC flows through an inductor.

**Statement 2** The inductive reactance increases as the frequency of an AC source decreases.

**Answer:** 3. Statement 1 is true and Statement 2 is false.

In an inductor, the current lags behind the voltage by \(\frac{\pi}{2}\).

Inductive reactance = X_{L} = ω_{L} = 2πfL increases with an increase in frequency.

**Question 3. Statement 1** The quantity L/R possesses a dimension of time.

**Statement 2** To reduce the rate, of increase of current through a solenoid, we should increase the time constant (L/R).

**Answer:** 2. Statement 1 is true; Statement 2 is true; but Statement 2 is not a correct explanation of Statement 1.

The induced emf in an inductor is \(|\varepsilon|=L \frac{d I}{d t}\) which has the dimensions of [I.R].

Thus, \(\left[\frac{L}{R}\right] \frac{d I}{d t}=[I]\)

So, \(\frac{L}{R}\) has dimention Of Time.

Further, \(\frac{d I}{d t}=\frac{I}{\left(\frac{L}{R}\right)}\)

To reduce \(\frac{d I}{d t}\) the value of \(\frac{L}{R}\) should be large.

**Question 4. Statement 1** In a series LCR circuit, the resonance occurs at one frequency only.

**Statement 2** At resonance, the inductive reactance is equal and opposite to the capacitive reactance.

**Answer:** 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.

At resonance, the circuit is purely resistive and has a single resonance frequency = \(f=\frac{1}{2 \pi \sqrt{L C}}\).

This corresponds to the equal and opposite values of the inductive reactance and capacitive reactance.

**Question 5. Statement 1** No power loss is associated with pure capacitors in an AC circuit.

Statement 2 No current flows in this circuit.

**Answer:** 3. Statement 1 is true and Statement 2 is false.

In an AC circuit with a pure capacitor, the phase difference between the current and the voltage is \(\frac{\pi}{2}\), so power dissipated \(\left(\frac{1}{2} I_0 V_0 \cos \frac{\pi}{2}\right)\) is zero.

**Question 6. Statement 1** At resonance, a series LCR circuit has a current.

**Statement 2** At resonance, in a series LCR circuit, the current and the emf are not in phase with each other.

**Answer:** 5. Both Statement 1 and Statement 2 are false.

At resonance, in an LCR circuit, the current is maximum since the impedance is minimum (=R). At resonance, the circuit is purely resistive, so the current. and the voltage is in the same phase.

**Question 7. Statement 1** Induction coils are usually made of a thick copper wire.

**Statement 2** Induced current is more in resistance.

**Answer:** 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.

Induction coils have high inductance and low resistance. For low resistance, the copper wire has to be thick. For more induced current, resistance has to be low according to Ohm’s law.

**Question 8. Statement 1** Transformers are used only in alternating current, not in direct current.

**Statement 2** Only alternating current can be stepped up or down by means of transformers.

**Answer:** 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.

With a DC source, the periodic change in magnetic flux does not occur to induce voltage in the secondary coil. Hence, only an AC source can be used to raise or lower the voltage by adjusting the turn ratio N_{s}/N_{p}.

**Question 9. Statement 1** We use a thick wire in the secondary coil of a stepdown transformer to reduce heat production.

**Statement 2** When the plane of the armature is parallel to the magnetic field lines, the magnitude of induced emf is maximum.

**Answer:** 2. Statement 1 is true; Statement 2 is true; but Statement 2 is not a correct explanation of Statement 1.

Thick wires have low resistance, hence there is less loss of energy by heat production.

Instantaneous magnetic flux linked with the coil of armature in a B-field is \(\phi=N \vec{A} \cdot \vec{B}=N A B \cos \theta\).

Induced emf = \(\varepsilon=-\frac{d \phi}{d t}=N A B \omega \sin \theta=\varepsilon_{\max } \sin \theta\)

Given, \(\theta=\frac{\pi}{2}\) so emf = maximum = NABω.

## Magnetism And Matter

**Question 1. Statement 1** We cannot think of a magnetic field configuration with three poles.

**Statement 2** A bar magnet does exert a torque on itself due to its own field.

**Answer: 2. Statement 1** is true; Statement 2 is true; but Statement 2 is not a correct explanation of Statement 1.

Monopolesin magnetism do not exist. Magnets always exist as dipoles. A system like a bar magnet can produce a magnetic field but does not experience a force or a torque in its own field.

**Question 2. Statement 1** Magnetic field lines are continuous and closed.

**Statement 2** Magnetic monopoles do not exist.

**Answer:** 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.

Magnetic field lines form a closed loop. This is a consequence of the nonexistence of magnetic monopole.

**Question 3. Statement 1** The magnetic force between two short magnets follows the inverse square law of distance when they are coaxial.

**Statement 2** The magnetic force between two poles does not follow the inverse square law of distance.

**Answer:** 5. Both Statement 1 and Statement 2 are false.

The magnetic force between two coaxial short magnets is given by \(F \propto \frac{1}{r^4}\). The reason is also false as magnetic force between two poles does follow the inverse square law of distance.

**Question 4. Statement 1** Magnetic susceptibility is a pure number.

**Statement 2** The value of magnetic susceptibility for vacuum is one.

**Answer:** 3. Statement 1 is true and Statement 2 is false.

Magnetic susceptibility % is the ratio of magnetization (= magnetic moment per unit volume) to the applied magnetizing field H. Both M and H have the same unit, so it is a pure number (dimensionless). Susceptibility for vacuum is zero since magnetization M in a vacuum is zero.

**Question 5. Statement 1** A superconductor is a perfect diamagnetic substance.

**Statement 2** A superconductor is a perfect conductor.

**Answer:** 2. Statement 1 is true; Statement 2 is true; but Statement 2 is not a correct explanation of Statement 1.

A superconductor is a perfect diamagnetic substance since in its interior the magnetic field \(\vec{B}\) = 0 and is completely screened. A superconductor is a perfect conductor as its resistance is zero.

**Question 6. Statement 1** The magnetic poles of Earth do not coincide with the geographical poles.

**Statement 2** The discrepancy between the orientation of a compass and true north-south direction is known as magnetic declination.

**Answer:** 2. Statement 1 is true; Statement 2 is true; but Statement 2 is not a correct explanation of Statement 1.

The axis about which the earth rotates passes through the geographical north and south poles whereas the magnetic axis of the earth (assumed to be a magnetized sphere) is somewhat inclined to the rotational axis. Magnetic declination is the angle between the magnetic meridian and the geographical meridian.

**Question 7. Statement 1** Diamagnetic materials can exhibit magnetism.

**Statement 2** Diamagnetic materials have permanent dipole moments.

**Answer:** 5. Both Statement 1 and Statement 2 are false.

Diamagnetic materials neither exhibit magnetism nor do they have permanent dipole moments.

**Question 8. Statement 1** The true geographic north directions were found by using a magnetic needle.

**Statement 2** The magnetic meridian of the earth is along the axis of rotation of the earth.

**Answer:** 5. Both Statement 1 and Statement 2 are false.

A magnetic needle is used to find the magnetic north but not the geographic north. A magnetic meridian is not aligned along the axis of rotation of the earth.

**Question 9. Statement 1** A ferromagnetic substance becomes paramagnetic above the Curie temperature.

**Statement 2** Domains are destroyed at high temperatures.

**Answer:** 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.

The Curie temperature is the temperature above which a ferromagnetic material becomes paramagnetic due to the breaking up of magnetic domains.

**Question 10. Statement 1** A disc-shaped magnet is levitated above a superconducting material that has been cooled by liquid nitrogen.

**Statement 2** Superconductors repel magnets.

**Answer:** 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.

Superconductors exist only below a certain critical temperature but above that temperature, they behave like normal materials. When a magnet is placed above a superconductor (which is cooled using liquid nitrogen), a magnetic field is induced within it which is exactly equal and opposite to the applied external magnetic field due to the magnet. The polarities are such that they repel each other and the repulsive force is enough to float the magnet.

**Question 11. Statement 1** In water, the value of the magnetic field decreases.

**Statement 2** Water is a diamagnetic substance.

**Answer:** 1. Statement 1 is true; Statement 2 is true; and Statement 2 is a correct explanation of Statement 1.

Water has relative permeability \(\left(\mu_{\mathrm{r}}=\frac{\mu}{\mu_0}\right)\) less than 1 and thus a negative magnetic susceptibility. Water is thus a diamagnetic substance in which magnetic field strength decreases.