Magnetism and Matter & EMI - Revision Session

Assertion : Two coaxial conducting rings of different radii are placed in space. The mutual inductance of both the rings maximum if the rings are coplanar.
Reason : For two coaxial conducting rings of different radii, the magnitude of magnetic flux in one ring due to current in other ring is maximum when both rings are coplanar

Given below are two statements:

Assertion (A):

No electric current will be present within a region having a uniform and constant magnetic field.

Reason (R):

Within a region of uniform and constant magnetic field

\vec{B}

the path integral of the magnetic field

φ \vec{B} . \vec{dl}

along any closed path is zero. Hence from ampere circuital law $\varphi \overrightarrow{\mathrm{B}} \cdot \overrightarrow{\mathrm{dl}}=\mu_0 1$ (where the given terms have usual meaning), no current can be present within a region having a uniform and constant magnetic field.

1.	Both (A) and (R) are true and (R) is the correct explanation of (A).
2.	Both (A) and (R) are true but (R) is not the correct explanation of (A).
3.	(A) is true but (R) is false.
4.	Both (A) and (R) are false.

Assertion: Two identical circulars closed loops made of copper and aluminium are withdrawn from the magnetic field with equal velocities. The induced emf is same but induced current is different.
Reason : Induced current depends on the resistance of the circuit.

Assertion: A resistance R is connected between the two ends of parallel smooth conducting rails. A conducting rod lies on these fixed horizontal rails and a uniform constant magnetic field B exists perpendicular to the plane of the rails as shown in the figure. If the rod is given a velocity v and released as shown in the figure, it will stop after some time. The total work done by the magnetic field is negative.

Reason: If a force acts opposite to the direction of velocity, its work done is negative.

Assertion : The poles of a magnet cannot be separated by breaking into two pieces.
Reason : The magnetic moment will be reduced to half when magnet is broken into two equal pieces

6. Given below are two statements:

Assertion (A):	If a compass needle is kept at the magnetic north pole of the earth, the compass needle may stay in any direction.
Reason (R):	The dip needle will stay vertical at the north pole of the earth.

1.	Both (A) and (R) are true and (R) is the correct explanation of (A).
2.	Both (A) and (R) are true but (R) is not the correct explanation of (A).
3.	(A) is true but (R) is false.
4.	Both (A) and (R) are false.

Given below are two statements:

Assertion (A):	The earth's magnetic field is due to iron present in its core.
Reason (R):	At a high-temperature magnet losses its magnetic property or magnetism.

1.	Both (A) and (R) are true and (R) is the correct explanation of (A).
2.	Both (A) and (R) are true but (R) is not the correct explanation of (A).
3.	(A) is true but (R) is false.
4.	Both (A) and (R) are false.

Assertion : The susceptibility of diamagnetic materials does not depend upon temperature.
Reason : Every atom of a diamagnetic material is not a complete magnet is itself.

A metallic rod of length is tied to a string of length 21 and made to rotate with angular speed won a horizontal table with one end of the string fixed. If there is a vertical magnetic field 'B' in the region, the e.m.f. induced across the ends of the rod is

1. $\frac{2 {Bωl}^{2}}{2}$
2. $\frac{3 {Bωl}^{2}}{2}$
3. $\frac{4 {Bωl}^{2}}{2}$
4. $\frac{5 {Bωl}^{2}}{2}$

10.

A simple pendulum with a bob of mass m and conducting wire of L swings under gravity through an angle 2 $θ$ . The earth's magnetic field component in the direction perpendicular to swing is B. Maximum potential difference induced across the pendulum is

1. $2 BL \sin (\frac{θ}{2}) {(gL)}^{1 / 2}$
2. $BL \sin (\frac{θ}{2}) (gL)$
3. $BL \sin (\frac{θ}{2}) {(gL)}^{3 / 2}$
4. $BL \sin (\frac{θ}{2}) {(gL)}^{2}$

11.

An inductor (L= 100 mH), a resistor (R = 100 $Ω$ ), and a battery (E = 100V) are initially connected in series as shown in the figure. After a long time, the battery is disconnected after short-circuiting the points A and B. The current in circuit 1 ms after the short circuit is

1. 1/A
2. eA
3. 0.1 A
4. 1A

12.

An inductor of inductance L = 400 mH and resistors of resistance of $R_{1} = 2 Ω$ and $R_{2} = 2 Ω$ are connected to a battery of emf 12 V as shown in the figure. The internal resistance of the battery is negligible. The switch S is closed at t = 0. The potential drop across Las function of time is

1. $\frac{12}{t} e^{- 3 t} V$
2. $6 (1 - e^{- t / 0.2}) V$
3. $12 e^{- 5 t} V$
3. $6 e^{- 5 t} V$

13.

A dip needle lies initially in the magnetic meridian when it shows an angle of dip $θ$ at a place. The dip circle is rotated through an angle x in the horizontal plane and then it shows an angle of dip $θ$ '. Then $\frac{\tan θ'}{\tan θ}$ is
1. 1/cos x
2. 1/sin x
3. 1/tan x
4. cos x

14.

The figure shows the various positions (labelled by subscripts) of small magnetised needles P and Q. The arrows show the direction of their magnetic moment. Which configuration corresponds to the lowest potential energy among all the configurations shown.

(1) PQ₃
(2) PQ₄
(3) PQ₅
(4) PQ₆

15.

Two tangent galvanometers A and B have coils of radii 8 cm and 16 cm respectively and resistance 8 $Ω$ each. They are connected in parallel with a cell of emf 4 V and negligible internal resistance. The deflections produced in the tangent galvanometers A and B are 30° and 60° respectively. If A has 2 turns, then B must have
1. 18 turns
2. 12 turns
3. 6 turns
4. 2 turns

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