Q: The magnetic flux through a plane surface of area A in a uniform field B, the normal making angle \theta with the field, is:

BA\cos\theta. Flux is the scalar product \vec{B}\cdot\vec{A}, greatest when the surface is perpendicular to the field.

Q: One weber is equivalent to:

1\text{ T}\cdot\text{m}^2. It is also one volt second, since an EMF of one volt corresponds to flux changing at one weber per second.

Q: The flux linked with a coil changes from 0.8\text{ Wb} to 0.2\text{ Wb} in 0.1\text{ s}. The induced EMF is:

6\text{ V}. |e| = \left|\dfrac{\Delta\Phi}{\Delta t}\right| = \dfrac{0.8 - 0.2}{0.1} = 6\text{ V}.

Q: A coil of 100 turns has flux changing at 0.02\text{ Wb}/\text{s}. The induced EMF is:

2\text{ V}. e = N\dfrac{d\Phi}{dt} = 100 \times 0.02 = 2\text{ V}.

Question 1

The magnetic flux through a plane surface of area A in a uniform field B, the normal making angle 	heta with the field, is:

Accepted Answer

BA\cos	heta. Flux is the scalar product \vec{B}\cdot\vec{A}, greatest when the surface is perpendicular to the field.

Question 2

Faraday's first law of electromagnetic induction states that:

Accepted Answer

An EMF is induced in a circuit whenever the magnetic flux linked with it changes. It is the change of flux, not its magnitude, that matters; a steady flux however large induces nothing.

Question 3

Faraday's second law gives the magnitude of the induced EMF in a coil of N turns as:

Accepted Answer

e = -N\dfrac{d\Phi}{dt}. The minus sign expresses Lenz's law: the induced EMF opposes the change producing it.

Question 4

The induced EMF in a circuit depends on:

Accepted Answer

The rate of change of magnetic flux. A large but constant flux induces no EMF, while a small flux changing rapidly induces a large one.

Question 5

The dimensional formula of magnetic flux is:

Accepted Answer

[M^1L^2T^{-2}A^{-1}]. \Phi = BA, and B = \dfrac{F}{IL}, giving \dfrac{[M^1L^1T^{-2}]}{[A][L]}[L^2] = [M^1L^2T^{-2}A^{-1}].

Question 6

The magnetic flux linked with a coil can be changed by:

Accepted Answer

Changing the field, the area, or the orientation of the coil. Since \Phi = BA\cos	heta, altering any of the three quantities changes the flux and induces an EMF.

Question 7

When the flux through an open (unclosed) coil changes:

Accepted Answer

An EMF is induced but no current flows. The EMF exists whenever the flux changes; a complete conducting path is needed only for the current.

Question 8

One weber is equivalent to:

Accepted Answer

1	ext{ T}\cdot	ext{m}^2. It is also one volt second, since an EMF of one volt corresponds to flux changing at one weber per second.

Question 9

The flux linked with a coil changes from 0.8	ext{ Wb} to 0.2	ext{ Wb} in 0.1	ext{ s}. The induced EMF is:

Accepted Answer

6	ext{ V}. |e| = \left|\dfrac{\Delta\Phi}{\Delta t}ight| = \dfrac{0.8 - 0.2}{0.1} = 6	ext{ V}.

Question 10

A coil of 100 turns has flux changing at 0.02	ext{ Wb}/	ext{s}. The induced EMF is:

Accepted Answer

2	ext{ V}. e = N\dfrac{d\Phi}{dt} = 100 	imes 0.02 = 2	ext{ V}.

Question 11

A coil of area 0.02	ext{ m}^2 lies perpendicular to a field of 0.5	ext{ T}. The flux through it is:

Accepted Answer

0.01	ext{ Wb}. \Phi = BA\cos 0^\circ = 0.5 	imes 0.02 = 0.01	ext{ Wb}.

Question 12

A coil of area 0.05	ext{ m}^2 has its normal at 60^\circ to a field of 0.4	ext{ T}. The flux through it is:

Accepted Answer

0.01	ext{ Wb}. \Phi = BA\cos 60^\circ = 0.4 	imes 0.05 	imes 0.5 = 0.01	ext{ Wb}.

Question 13

A coil of 50 turns experiences a flux change of 0.5	ext{ Wb} in 0.2	ext{ s}. The induced EMF is:

Accepted Answer

125	ext{ V}. e = N\dfrac{\Delta\Phi}{\Delta t} = 50 	imes \dfrac{0.5}{0.2} = 125	ext{ V}.

Question 14

A coil of 200 turns and area 0.01	ext{ m}^2 has the field through it changed from 0.1	ext{ T} to 0.5	ext{ T} in 0.2	ext{ s}. The induced EMF is:

Accepted Answer

4	ext{ V}. e = NA\dfrac{\Delta B}{\Delta t} = 200 	imes 0.01 	imes \dfrac{0.4}{0.2} = 4	ext{ V}.

Question 15

A coil of 100 turns and resistance 10\,\Omega has its flux changed by 0.01	ext{ Wb}. The charge that flows is:

Accepted Answer

0.1	ext{ C}. q = \dfrac{N\Delta\Phi}{R} = \dfrac{100 	imes 0.01}{10} = 0.1	ext{ C}, independent of how fast the change occurs.

Question 16

The flux through a coil varies as \Phi = 5t^2	ext{ weber}. The induced EMF at t = 2	ext{ s} is:

Accepted Answer

20	ext{ V}. e = \dfrac{d\Phi}{dt} = 10t. At t = 2	ext{ s}, e = 20	ext{ V}.

Question 17

The flux through a coil varies as \Phi = (3t + 4)	ext{ weber}. The induced EMF is:

Accepted Answer

3	ext{ V}, constant in time. e = \dfrac{d\Phi}{dt} = 3	ext{ V}; the constant term contributes nothing.

Question 18

A coil of area 0.1	ext{ m}^2 in a field of 0.2	ext{ T} is rotated from a position perpendicular to the field to one parallel to it in 0.5	ext{ s}. The average induced EMF is:

Accepted Answer

0.04	ext{ V}. The flux falls from 0.02	ext{ Wb} to zero, so e = \dfrac{0.02}{0.5} = 0.04	ext{ V}.

Question 19

A coil of area 0.04	ext{ m}^2 lies with its plane perpendicular to a field of 0.3	ext{ T}. The flux through it is:

Accepted Answer

0.012	ext{ Wb}. \Phi = BA = 0.3 	imes 0.04 = 0.012	ext{ Wb}.

Question 20

A coil of 500 turns has its flux changed by 0.004	ext{ Wb} in 0.01	ext{ s}. The induced EMF is:

Accepted Answer

200	ext{ V}. e = 500 	imes \dfrac{0.004}{0.01} = 500 	imes 0.4 = 200	ext{ V}.

Magnetic Flux & Faraday's Laws — MH-CET Physics MCQs with Solutions

Questions with solutions