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A flexible circular loop $20 cm$ in diameter lies in a magnetic field of magnitude $B = 1 T$ , directed into the plane of page as shown. The loop is pulled at the points indicated by the arrows forming a loop of zero area in $0.314 \sec$ . The average $emf$ induced (in $mV$ ) in the loop is.

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Important Questions on Electromagnetic Induction

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Physics>Electricity and Magnetism>Electromagnetic Induction>Production of Induced EMF

A conducting metal circular-wire-loop of radius

r

is placed perpendicular to a magnetic field which varies with time as

B = B_{0} e^{- \frac{t}{τ}},

where

B_{0} and τ

are constants at time

t = 0

. If the resistance of the loop is

R

, then the heat generated in the loop after a long time

(t \to \infty)

EASY

Physics>Electricity and Magnetism>Electromagnetic Induction>Production of Induced EMF

An electron moves on a straight line path XY as shown. The abcd is a coil adjacent to the path of electron. What will be the direction of current, if any, induced in the coil?

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EASY

Physics>Electricity and Magnetism>Electromagnetic Induction>Production of Induced EMF

A long solenoid of diameter

0.1 m

has

2 \times 10^{4}

turns per meter. At the centre of the solenoid, a coil of

100

turns and radius

0.01 m

is placed with its axis coinciding with the solenoid axis. The current in the solenoid reduces at a constant rate to

0 A

from

4 A

0.05 s

. If the resistance of the coil is

10 π^{2} Ω,

the total charge flowing through the coil during this time is

HARD

Physics>Electricity and Magnetism>Electromagnetic Induction>Production of Induced EMF

A circular loop of radius

0.3 cm

lies parallel to a much bigger circular loop of radius

20 cm

. The centre of the small loop is on the axis of the bigger loop. The distance between their centres is

15 cm

. If a current of

2.0 A

flows through the smaller loop, then the flux linked with a bigger loop is:

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Physics>Electricity and Magnetism>Electromagnetic Induction>Production of Induced EMF

A uniform magnetic field is restricted within a region of radius,

r .

The magnetic field changes with time at a rate,

\frac{d \vec{B}}{d t}

. Loop one of radius

R > r

encloses the region,

r

and loop two of radius,

R

is outside the region of magnetic field as shown in the figure below. Then the emf generated is

Question Image

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Physics>Electricity and Magnetism>Electromagnetic Induction>Production of Induced EMF

800

turn coil of the effective area

0.05 m^{2}

is kept perpendicular to the magnetic field

5 \times 10^{- 5} T .

When the plane of the coil is rotated by

90^{o}

around any of its coplanar axis in

0.1 s,

the emf induced in the coil will be:

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Physics>Electricity and Magnetism>Electromagnetic Induction>Production of Induced EMF

The figure shows a bar magnet and a metallic coil. Consider four situations. (I) Moving the magnet away from the coil. (II) Moving the coil towards the magnet. (III) Rotating the coil about the vertical diameter. (IV) Rotating the coil about its axis.

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An emf in the coil will be generated for the following situations.

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Physics>Electricity and Magnetism>Electromagnetic Induction>Production of Induced EMF

Consider a circular coil of wire carrying constant current

I,

forming a magnetic dipole. The magnetic flux through an infinite plane that contains the circular coil and excluding the circular coil area is given by

ϕ_{i}

The magnetic flux through the area of the circular coil area is given by

ϕ_{0}

. Which of the following option is correct?

EASY

Physics>Electricity and Magnetism>Electromagnetic Induction>Production of Induced EMF

A coil of cross-sectional area

A

having

n

turns is placed in a uniform magnetic field

B

. When it is rotated with an angular velocity

ω,

the maximum e.m.f. induced in the coil will be:

MEDIUM

Physics>Electricity and Magnetism>Electromagnetic Induction>Production of Induced EMF

A conducting bar of mass

m

and length

l

moves on two frictionless parallel rails in the presence of a constant uniform magnetic field of magnitude

B

directed into the page as shown in the figure.The bar is given an initial velocity

v_{0}

towards the right at

t = 0 .

Then, the

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Physics>Electricity and Magnetism>Electromagnetic Induction>Production of Induced EMF

A very long solenoid of radius

R

is carrying current

I (t) = k t e^{- α t} (k > 0),

as a function of time

(t \geq 0) .

Counterclockwise current is taken to be positive. A circular conducting coil of radius

2 R

is placed in the equitorial plane of the solenoid and concentric with the solenoid. The current induced in the outer coil is correctly depicted, as a function of time, by:

HARD

Physics>Electricity and Magnetism>Electromagnetic Induction>Production of Induced EMF

A square-shaped conducting wire loop of dimension a moving parallel to the $x$ -axis approaches a square region of size $b (a < b)$ where a uniform magnetic field $B$ exists pointing into the plane of the paper (see figure). As the loop passes through this region, the plot correctly depicting its speed $(v)$ as a function of $x$ is.

Question Image

HARD

Physics>Electricity and Magnetism>Electromagnetic Induction>Production of Induced EMF

A long solenoid of radius

R

carries a time

(t)

dependent current

I (t) = I_{0} t (1 - t)

. A ring of radius

2 R

is placed coaxially near its middle. During the time interval

0 \leq t \leq 1,

the induced current

(I_{R})

and the induced

E M F (V_{R})

in the ring change as:

EASY

Physics>Electricity and Magnetism>Electromagnetic Induction>Production of Induced EMF

A loop

A B C D E F A

of straight edges has six corner points

A (0, 0, 0), B (5, 0, 0), C (5, 5, 0), D (0, 5, 0), E (0, 5, 5)

and

F (0, 0, 5)

. The magnetic field in this region is

\vec{B} = (3 \hat{i} + 4 \hat{k}) T

. The quantity of flux through the loop

A B C D E F A

(in

W b

) is _____________

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Physics>Electricity and Magnetism>Electromagnetic Induction>Production of Induced EMF

At time

t = 0

magnetic field of

1000 G a u s s

is passing perpendicularly through the area defined by the closed loop shown in the figure. If the magnetic field reduces linearly to

500 G a u s s,

in the next

5 s,

then induced

E M F

in the loop is:
Question Image

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Physics>Electricity and Magnetism>Electromagnetic Induction>Production of Induced EMF

The relation between the charge flow

ΔQ

through the circuit of resistance

r

and the change in the magnetic flux

{Δϕ}_{B}

MEDIUM

Physics>Electricity and Magnetism>Electromagnetic Induction>Production of Induced EMF

A planar loop of wire rotates in a uniform magnetic field. Initially, at

t = 0

, the plane of the loop is perpendicular to the magnetic field. If it rotates with a period of

10 s

about an axis in its plane then the magnitude of induced emf will be maximum and minimum, respectively at:

EASY

Physics>Electricity and Magnetism>Electromagnetic Induction>Production of Induced EMF

In a coil of resistance $100 Ω$ , a current is induced by changing the magnetic flux through it as shown in the figure. The magnitude of change in flux through the coil is:
Question Image

HARD

Physics>Electricity and Magnetism>Electromagnetic Induction>Production of Induced EMF

A conducting square frame of side

a

and a long straight wire carrying current

I

are located in the same plane as shown in the figure. The frame moves to the right with a constant velocity

V

. The e.m.f induced in the frame (when the centre of the frame is at a distance

x

from the wire) will be proportional to :
Question Image

EASY

Physics>Electricity and Magnetism>Electromagnetic Induction>Production of Induced EMF

When the current in a coil changes from

5 A

2 A

0 .1 s

, an average voltage of

50 V

is produced. The self-inductance of the coil is

A flexible circular loop 20 cm in diameter lies in a magnetic field of magnitude B=1 T , directed into the plane of page as shown. The loop is pulled at the points indicated by the arrows forming a loop of zero area in 0.314 sec. The average emf induced (in mV) in the loop is.

Important Questions on Electromagnetic Induction

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A flexible circular loop $20 cm$ in diameter lies in a magnetic field of magnitude $B = 1 T$ , directed into the plane of page as shown. The loop is pulled at the points indicated by the arrows forming a loop of zero area in $0.314 \sec$ . The average $emf$ induced (in $mV$ ) in the loop is.