Electromagnetic Induction Test

Result

Electromagnetic Induction Test - 16

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Question 1
1 / -0

A square of side L metres lies in the xy-plane in a region, where the magnetic field is given by \(B=B_0(2\hat i+3\hat j+4\hat k)\) T, where \(B_0\) is constant. The magnitude of flux passing through the square is

A
\( 2B_0L^2Wb\)

B
\(3B_0L^2Wb\)

C
\(4B_0L^2Wb\)

D
\(\sqrt{ 29}B_0L^2Wb\)

Solution

As we know that, the magnetic flux linked with uniform surface of area A in uniform magnetic field is \(\phi\) = B.A

The direction of A is perpendicular to the plane of square and square line in x-y plane in a region.

A = \(L^2\hat k\)

As given that, \(B=B_0(2\hat i+3\hat j+4\hat k)\)

So, \(\phi\) = B.A = \(B_0(2\hat i+3\hat j+4\hat k).L^2\hat k\)

= \(4B_0L^2\,\,Wb\).
Question 2
1 / -0

The self inductance L of a solenoid of length l and area of cross-section A, with a fixed number of turns N increases as

A
l and A increase

B
l decreases and A increases

C
l increases and A decreases

D
both l and A decrease

Solution

The self-inductance of a long solenoid of cross-sectional area A and length l, having n turns per unit length, filled the inside of the solenoid with a material of relative permeability is given by

L = \(\mu_r\mu_0n^2Al\)

\(\therefore\) n = \(N\over l\)

L = \(\mu_r\mu_0\Big[{N^2.A\over l.l}\Big].l\)

L = \(\mu_r\mu_0[{N^2A\over l}]\) \(\Big(L\propto A,L\propto {1\over l}\Big)\)

As \(\mu_r\) and N are constant here so, to increase L for a coil, area A must be increased and l must be decreased.
Question 3
1 / -0

A metal plate is getting heated. It can be because

(a) a direct current is passing through the plate

(b) it is placed in a time varying magnetic field

(c) it is placed in a space varying magnetic field, but does not vary with time

(d) a current (either direct or alternating) is passing through the plate

A
(b),(c),(d)

B
(a),(c),(d)

C
(a),(b),(d)

D
(a),(b),(c)

Solution

A plate or conductor is getting heated when a DC or AC current is passed due to heating effect of electric current (H = \(I^2\)Rt). Also, when metal plate is subjected to time varying magnetic field, the magnetic flux linked with the plate changes and eddy currents comes into existence which make the heating of plate take place.
Question 4
1 / -0

An emf is produced in a coil, which is not connected to an external voltage source. This can be due to

(a) the coil being in a time varying magnetic field

(b) the coil moving in a time varying magnetic field

(c) the coil moving in a constant magnetic field

(d) the coil is stationary in external spatially varying magnetic field, which does not change with time

A
(b),(c),(d)

B
(a),(c),(d)

C
(a),(b),(d)

D
(a),(b),(c)

Solution

emf produced in coil due to change in magnetic flux with time or magnetic flux linked with the isolated coil change when the coil being in a time varying magnetic field, the coil moving in a constant magnetic field or in time varying magnetic field.
Question 5
1 / -0

A circular coil expands radially in a region of magnetic field and no electromotive force is produced in the coil. This can be because

(a) the magnetic field is constant

(b) the magnetic field is in the same plane as the circular coil and it may or may not vary

(c) the magnetic field has a perpendicular (to the plane of the coil) component whose magnitude is decreasing suitably

(d) there is a constant magnetic field in the perpendicular (to the plane of the coil) direction

A
(a),(b)

B
(b),(c)

C
(c),(d)

D
(d),(a)

Solution

When circular coil expands in the region of magnetic field such that when it is in the same plane as the circular coil or the magnetic field has a perpendicular to the plane of the coil component whose magnitude is decreasing suitably so that the cross product of magnetic field and surface area of plane of coil remain constant at every instant.