Electromagnetic Induction Test

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Electromagnetic Induction Test - 36

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Weekly Quiz Competition

Question 1
1 / -0

When the current in a coil changes from 2 amp. to 4 amp. in 0.05 sec., an e.m.f. of 8 volt induced in the coil. The coefficient of self inductance of the coil is

A
0.1 henry

B
0.2 henry

C
0.4 henry

D
0.8 henry

Solution

Induced e.m.f. $$\epsilon=\dfrac {d\phi}{dt}$$

$$=\dfrac {dBA}{dt}=A_0\dfrac {dB}{dt}$$

$$=A_0\left (\dfrac {4B_0-B_0}{t}\right )=3A_0B_0/t$$
Question 2
1 / -0

A copper disc of radius $$0.1$$ $$m$$ rotated about its centre with $$10$$ revolutions per second in a uniform magnetic field of $$0.1$$ tesla with it's plane perpendicular to the field. The e.m.f. induced across the radius of disc is:

A
$$\dfrac {\pi}{10}volt$$

B
$$\dfrac {2\pi}{10}volt$$

C
$$\pi \times 10^{-2}volt$$

D
$$2\pi \times 10^{-2}volt$$

Solution

Consider a small radial segment of $$dx$$ at a distance $$x$$ from the centre of the disc. Velocity of this segment is $$\omega x$$. Emf induced across this segment
$$de=vBL=\omega xB dx$$
Total emf induced across radius of disc $$r$$

$$E=\dfrac{1}{2}B\omega r^2$$

As $$\omega=2\pi n$$ where $$n$$ is number of revolutions per second

$$ B=0.1 T, r=0.1 m, \omega=10 rev/s=20\pi rad/s $$

$$ E=\dfrac 12 \times 0.1 \times 0.01 \times 20\pi=\pi \times 10^{-2} V $$
Question 3
1 / -0

Magnetic flux $$\phi$$, in weber, in a closed circuit of resistance $$10\Omega$$ varies with time $$t$$ in seconds as $$\phi=6t^2-5t+1$$. The magnitude of induced current at $$t=0.25 s$$ is :

A
0.2 A

B
0.6 A

C
1.2 A

D
0.8 A

Solution

$$e=\dfrac {-d\phi}{dt}=\dfrac {-d}{dt}(6t^2-5t+1)=-12t+5$$

$$e=-12(0.25)+5=2 volt$$

$$i=\dfrac {e}{R}=\dfrac {2}{10}=0.2 A$$.
Question 4
1 / -0

The coefficient of mutual inductance between two coils depends on

A
medium between the coils

B
separation between the two coils

C
orientation of the two coils

D
all of the above

Solution

The flux linked with two coils will depend upon the angle between the two coils. If their planes are parallel, then magnetic flux from one would completely pass through the other. If the planes are perpendicular, no flux due to any of the coils would flow through the other.
The size of the two coils may be different which will affect the number of lines crossing the coil. The medium, if magnetic, will concentrate the field lines. Thus, all parameters would affect the inductance between them.
Question 5
1 / -0

The current in a coil of $$L=40 mH$$ is to be increased uniformly from $$1A$$ to $$11A$$ in $$4$$ milliseconds. The induced e.m.f. will be

A
$$100 V$$

B
$$0.4V$$

C
$$440 V$$

D
$$40V$$

Solution

$$e=\dfrac {LdI}{dt}$$

$$=\dfrac {40\times 10^{-3}(11-1)}{4\times 10^{-3}}$$

$$=100V$$
Question 6
1 / -0

A student connects a coil of wire with a sensitive galvanometer as shown in figure. He will observe the deflection in the galvanometer if bar magnet is:

A
one of the facts of the coil placed near and parallel to the axis of the coil

B
placed near one of the facts of the coil and perpendicular to the axis of the coil

C
placed inside the coil

D
moved towards or away from the coil parallel to the axis of the coil

Solution
Question 7
1 / -0

A square loop of side a is rotating about its diagonal with angular velocity $$\omega$$ in a perpendicular magnetic field $$\vec B$$. It has 10 turns. The emf induced is

A
$$B a^2 sin \omega t$$

B
$$B a^2 cos \omega t$$

C
$$5\sqrt 2 Ba^2$$

D
$$10 B a^2 sin \omega t$$

Solution

$$\phi=nBA cos\theta =10 Ba^2 cos\omega t$$

$$e=-\dfrac {d\phi}{dt}$$

$$=-\dfrac {d}{dt}(10 Ba^2 cos \omega t)$$

$$=10 Ba^2 sin\omega t(\omega)$$
Question 8
1 / -0

A horizontal telegraph wire $$0.5\ km$$ long running east and west in a part of a circuit whose resistance is $$2.5\ \Omega$$. The wire falls to $$g=10.0\ m/s^2$$ and $$B=2\times 10^{-5} weber/m^2$$, then the current induced in the circuit is

A
$$0.7\ amp$$

B
$$0.04\ amp$$

C
$$0.02\ amp$$

D
$$0.01\ amp$$

Solution

$$i=\dfrac {\varepsilon}{R}=\dfrac {1}{R}\dfrac {d\phi}{dt}$$

Here $$df=B\times A=(2\times 10^{-5})\times 0.5\times 10^{+3}\times 5)$$

$$dt=$$ time taken by the wire to fall at ground

$$=(2h/g)^{1/2}=(10/10)^{1/2}=1 sec$$

$$\therefore i=\dfrac {1}{2.5}\left [\dfrac {(2\times 10^{-5})\times (0.5\times 10^3\times 5)}{1}\right ]=0.02 amp$$.
Question 9
1 / -0

Which of the following units denotes the dimension $$\dfrac {ML^2}{Q^2}$$ where Q denotes the electric charge?

A
$$Wb/m^2$$

B
$$henry (H)$$

C
$$H/m^2$$

D
$$weber (Wb)$$

Solution

Mutual inductance $$=\dfrac {\phi}{I}=\dfrac {BA}{I}$$

$$[Henry]=\dfrac {[MT^{-1}Q^{-1}L^2]}{[QT^{-1}]}=ML^2Q^{-2}$$
Question 10
1 / -0

A wire loop is rotated in a uniform magnetic field about an axis perpendicular to the field. The direction of the current induced in the loop reverse once each

A
quarter revolution

B
half revolution

C
full revolution

D
two revolution

Solution

It is because after every 1/2 revolution the current becomes zero and mode of change in flux changes thereafter (If before the current becomes zero, the mode of flux change was from left to right then after the current becomes zero the mode of flux change becomes right to left).

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Electromagnetic Induction Test - 36

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Question 1

0.1 henry

0.2 henry

0.4 henry

0.8 henry

Solution

Question 2

$$\dfrac {\pi}{10}volt$$

$$\dfrac {2\pi}{10}volt$$

$$\pi \times 10^{-2}volt$$

$$2\pi \times 10^{-2}volt$$

Solution

Question 3

0.2 A

0.6 A

1.2 A

0.8 A

Solution

Question 4

medium between the coils

separation between the two coils

orientation of the two coils

all of the above

Solution

Question 5

$$100 V$$

$$0.4V$$

$$440 V$$

$$40V$$

Solution

Question 6

one of the facts of the coil placed near and parallel to the axis of the coil

placed near one of the facts of the coil and perpendicular to the axis of the coil

placed inside the coil

moved towards or away from the coil parallel to the axis of the coil

Solution

Question 7

$$B a^2 sin \omega t$$

$$B a^2 cos \omega t$$

$$5\sqrt 2 Ba^2$$

$$10 B a^2 sin \omega t$$

Solution

Question 8

$$0.7\ amp$$

$$0.04\ amp$$

$$0.02\ amp$$

$$0.01\ amp$$

Solution

Question 9

$$Wb/m^2$$

$$henry (H)$$

$$H/m^2$$

$$weber (Wb)$$

Solution

Question 10

quarter revolution

half revolution

full revolution

two revolution

Solution

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