Electromagnetic Induction Test

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Electromagnetic Induction Test - 5

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Question 1
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A rectangular conductor PQRS in which the conductor PQ is free to move is kept in a magnetic field B ,which is perpendicular to the PQRS which lies in a single plane. If the conductor PQ has a length l,moves with a speed v, then induced emf is

A
Blv.

B
Bv/l

C
Bl/v

D
Bv

Solution
Question 2
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A 500-loop circular wire coil with radius 4.00 cm is placed between the poles of a large electromagnet. The magnetic field is uniform and makes an angle of 60^∘ with the plane of the coil; it decreases at 0.200 T/s . Magnitude of induced emf is

A
0.475 V

B
0.495 V

C
0.455 V

D
0.435 V

Solution
Question 3
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Use Lenz ’s law to determine the direction of induced current in the situations described by the Figure (a) A wire of irregular shape turning into a circular shape; (b) A circular loop being deformed into a narrow straight wire. The directions for (a) and (b) respectively are

A
anti-clockwise,anti-clockwise .

B
clockwise,anti-clockwise

C
anti-clockwise,clockwise

D
clockwise,clockwise

Solution

Explanation:(a) for a given Periphery the area of a circle is maximum. When a coil takes a circular shape, the magnetic flux linked with the coil increases, so the current induced in the coil will tend to decrease the flux and so it will produce a magnetic field upward. As a result the current induced in the coil will flow in anticlockwise direction.(b) When circular coil takes the shape of narrow straight wire, The magnetic flux linked with the coil decreases. So the current induced in the coil will tend to oppose the decrease in magnetic flux. Hence it will produce an upward magnetic field so that the current induced in the coil will flow in anticlockwise direction.
Question 4
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An air-cored solenoid with length 30 cm, area of cross-section 25 cm² and number of turns 500, carries a current of 2.5 A. The current is suddenly switched off in a brief time of 10⁻³ s. Average back emf induced across the ends of the open switch in the circuit is

A
6.5 V .

B
4.6 V

C
4.5 V

D
5 V3.

Solution
Question 5
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If two coils of inductances L₁ and L₂ are linked such that their mutual inductance is M, then

A
The maximum value of M is √(L₁ L₂ )

B
M=L₁ −L₂ M=L₁ −L₂

C
M=L₁ ×L₂ M=L₁ ×L₂

D
M=L₁ +L₂

Solution

M=k √L₁ L₂

here k is cofficient of coupling. Its maximum value is 1 for tight coupling.
Question 6
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Eddy Currents are

A
plasma currents

B
induced solar currents that circulate throughout a river and are swirling .

C
gaseous currents

D
induced currents that circulate throughout the volume of a material similar to swirling eddies in a river.

Solution

Explanation:Eddy currents (also called Foucault currents) are loops of electrical current induced within conductors by a changing magnetic field in the conductor, due to Faraday 's law of induction. Eddy currents flow in closed loops within conductors, in planes perpendicular to the magnetic field. By lenz 's law an eddy current creates a magnetic field that opposes a change in the magnetic field that created it, and thus eddy currents react back on the source of the magnetic field.
Question 7
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Polarity of the capacitor in the situation described by the adjacent figure is

A
A will become negative with respect to B

B
Both A and B will become negative

C
Both A and B will become positive

D
A will become positive with respect to B

Solution

Explanation:A will become positive with respect to B because current indused is in clockwise direction
Question 8
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A 1.0 m long metallic rod is rotated with an angular frequency of 400 rad s⁻¹ about an axis normal to the rod passing through its one end. The other end of the rod is in contact with a circular metallic ring. A constant and uniform magnetic field of 0.5 T parallel to the axis exists everywhere. Emf developed between the centre and the ring is

A
120 V

B
100 V .

C
200 V

D
150 V

Solution
Question 9
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On a cylindrical rod two coils are wound one above the other. What is the coefficient of mutual inductance if the inductance of each coil os 0.1H?

A
0.15H

B
0.05H

C
0.20H

D
0.10H

Solution

As one coil is wound over the other so that coupling is tight i.e. k=1
Question 10
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Two ends of a horizontal conducting rod of length l are joined to a voltmeter. The whole arrangement moves with a horizontal velocity v, the direction of motion being perpendicular to the rod. Vertical component of the earth 's magnetic field is B. The voltmeter reads

A
Blv only if the rod moves eastward

B
Blv if the rod moves in any direction

C
Zero

D
Blv only if the rod moves westward

Solution