A fighter plane of length 20 m, wing span (distance from tip of one wing to the tip of the other wing) of 15 m and height 5 m is flying towards east over Delhi. Its speed is 240 m s - 1 . The earth's magnetic field over Delhi is 5 × 10 - 5 T with the declination angle ~ 0 o and dip of θ such that sin ⁡ θ = 2 3 . If the voltage developed is V B between the lower and upper side of the plane and V W between the tips of the wings then V B a n d V W are close to :

V B = 45 m V ; V W = 120 m V with left side of pilot at higher voltage

V B = 40 m V ; V W = 135 m V with left side of pilot at higher voltage

V B = 45 m V ; V W = 120 m V with right side of pilot at higher voltage

V B = 40 m V ; V W = 135 m V with right side of pilot at high voltage

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A wire is bent to form a semicircle of radius $a$ . The wire rotates about its one end with angular velocity $ω$ . Axis of rotation being perpendicular to the plane of the semicircle. In the space, a uniform magnetic field of induction $B$ exists along the axis of rotation, as shown in figure. Then

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Important Questions on Electromagnetic Induction

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Physics>Electricity and Magnetism>Electromagnetic Induction>Motional EMF

A solid metal cube of edge length

2 cm

is moving in the positive

y

-direction, at a constant speed of

6 m s^{- 1}

. There is a uniform magnetic field of

0 .1 T

in the positive

z

-direction. The potential difference between the two faces of the cube, perpendicular to the

x

-axis, is

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Physics>Electricity and Magnetism>Electromagnetic Induction>Motional EMF

The figure shows a square loop

L

of side

5 c m

which is connected to a network of resistances. The whole setup is moving towards the right with a constant speed of

1 c m s^{- 1}

. At some instant, a part of

L

is in a uniform magnetic field of

1 T

perpendicular to the plane of the loop. If the resistance of

L

1.7 Ω,

the current in the loop at that instant will be close to:
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MEDIUM

Physics>Electricity and Magnetism>Electromagnetic Induction>Motional EMF

A train is running at a speed of

72 km {hr}^{- 1}

on the rails separated by a distance of

150 cm .

If the vertical component of earth's magnetic field at the place is

4.0 \times 10^{- 5} T

The induced emf on the rails is

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Physics>Electricity and Magnetism>Electromagnetic Induction>Motional EMF

10 m

long horizontal wire extends from North East to South West. It is falling with a speed of

5.0 m s^{- 1},

at right angles to the horizontal component of the earth's magnetic field of

0.3 \times 10^{- 4} Wb m^{- 2} .

The value of the induced emf in the wire is:

HARD

Physics>Electricity and Magnetism>Electromagnetic Induction>Motional EMF

A fighter plane of length 20 m, wing span (distance from tip of one wing to the tip of the other wing) of 15 m and height 5 m is flying towards east over Delhi. Its speed is

240 m s^{- 1} .

The earth's magnetic field over Delhi is

5 \times 10^{- 5} T

with the declination angle

~ 0^{o}

and dip of

θ

such that

\sin θ = \frac{2}{3} .

If the voltage developed is

V_{B}

between the lower and upper side of the plane and

V_{W}

between the tips of the wings then

V_{B} a n d V_{W}

are close to :

MEDIUM

Physics>Electricity and Magnetism>Electromagnetic Induction>Motional EMF

A rod of length $2 m$ slides with a speed of $5 m s^{- 1}$ on a rectangular conducting frame as shown in figure. There exists a uniform magnetic field of $0.04 T$ perpendicular to the plane of the figure. If the resistance of the rod is $3 Ω$ . The current through the rod is

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Physics>Electricity and Magnetism>Electromagnetic Induction>Motional EMF

Consider the situation given in figure. The wire $A B$ slides on the fixed rails with a constant velocity. If the wire $A B$ is replaced by a semicircular wire, the magnitude of the induced current will:

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MEDIUM

Physics>Electricity and Magnetism>Electromagnetic Induction>Motional EMF

A jet plane with a wing-span of

25 m

is travelling horizontally towards the east with a speed of

3600 km / hour

. If the Earth's magnetic field at the location is

4 \times 10^{- 4} T

and the angle of dip is

30 °

, then, the potential difference between the ends of the wing is

MEDIUM

Physics>Electricity and Magnetism>Electromagnetic Induction>Motional EMF

A metallic rod of length $l$ is tied to a string of length $2 l$ and made to rotate with angular speed $ω$ on a horizontal table with one end of the string fixed. If there is a vertical magnetic field B in the region, the e.m.f. induced across the ends of the rod is:

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HARD

Physics>Electricity and Magnetism>Electromagnetic Induction>Motional EMF

A thin strip $10 c m$ long is on a $U$ shaped wire of negligible resistance and it is connected to a spring of spring constant $0.5 N m^{- 1}$ (see figure). The assembly is kept in a uniform magnetic field of $0.1 T .$ If the strip is pulled from its equilibrium position and released, the number of oscillations it performs before its amplitude decreases by a factor of $e$ is $N$ . If the mass of the strip is $50$ grams, its resistance $10 Ω$ and air drag negligible, $N$ will be close to:
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Physics>Electricity and Magnetism>Electromagnetic Induction>Motional EMF

Two straight conducting rails form a right angle as shown below. A conducting bar in contact with the rails starts at the vertex at time

t = 0

and moves with constant velocity of

v = 5 m s^{- 1}

along them. A magnetic field with

B = 0.1 T

is directed out of the page. The absolute value of the

emf

around the triangle at the time

t = 4 s

will be?

HARD

Physics>Electricity and Magnetism>Electromagnetic Induction>Motional EMF

A square frame of side $10 cm$ and a long straight wire carrying current $1 A$ are in the plane of the paper. Starting from close to the wire, the frame moves towards the right with a constant speed of $10 m s^{- 1}$ (see figure). The e.m.f induced at the time the left arm of the frame is at $x = 10 cm$ from the wire is

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HARD

Physics>Electricity and Magnetism>Electromagnetic Induction>Motional EMF

As shown in the figure, a rectangular loop of a conducting wire is moving away with a constant velocity $v$ in a perpendicular direction from a very long straight conductor carrying a steady current $I$ . When the breadth of the rectangular loop is very small compared to its distance from the straight conductor, how does the emf: $E$ induced in the loop vary with time $t ?$

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MEDIUM

Physics>Electricity and Magnetism>Electromagnetic Induction>Motional EMF

A wheel with

20

metallic spokes each

1 m

long is rotated with a speed of

120 rpm

in a plane perpendicular to a magnetic field of

0.4 G .

The induced emf between the axle and rim of the wheel will be,

(1 G = 10^{- 4} T)

EASY

Physics>Electricity and Magnetism>Electromagnetic Induction>Motional EMF

A horizontal rod of length $L$ rotates about a vertical axis with a uniform angular velocity $ω$ . A uniform magnetic field $B$ exists parallel to the axis of rotation. Then potential difference between the two ends of the rod is

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EASY

Physics>Electricity and Magnetism>Electromagnetic Induction>Motional EMF

An aeroplane, with its wings spread

10 m,

is flying at a speed of

180 km h^{- 1}

in a horizontal direction. The total intensity of earth's field at that part is

2.5 \times 10^{- 4} Wb m^{- 2}

and the angle of dip is

60 ° .

The EMF induced between the tips of the plane wings will be

EASY

Physics>Electricity and Magnetism>Electromagnetic Induction>Motional EMF

A bicycle generator creates

1.5 V

15 km h^{- 1}

. The EMF generated at

10 km h^{- 1}

is:

HARD

Physics>Electricity and Magnetism>Electromagnetic Induction>Motional EMF

10 c m

long perfectly conducting wire

P Q

is moving, with a velocity

1 c m / s

on a pair of horizontal rails of zero resistance. One side of the rails is connected to an inductor

L = 1 m H

and a resistance

R = 1 Ω

as shown in figure. The horizontal rails,

L

and

R

lie in the same plane with a uniform magnetic field

B = 1 T

perpendicular to the plane. If the key

S

is closed at certain instant, the current in the circuit after

1

milli second is

x \times 10^{- 3} A,

where the value of

x

is_______.
[Assume the velocity of wire

P Q

remains constant

(1 c m / s)

after key

S

is closed. Given:

e^{- 1} = 0.37,

where

e

is base of the natural logarithm]

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HARD

Physics>Electricity and Magnetism>Electromagnetic Induction>Motional EMF

Consider a thin metallic sheet perpendicular to the plane of the paper moving with speed

v

in a uniform magnetic field

B

going into the plane of the paper (see figure). If charge densities

σ_{1}

and

σ_{2}

are induced on the left and right surfaces respectively of the sheet, then (ignore fringe effects)

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MEDIUM

Physics>Electricity and Magnetism>Electromagnetic Induction>Motional EMF

A straight conductor of length

0.4 m

is moving with a speed of

7 {ms}^{- 1}

perpendicular to the magnetic field of intensity of

0.9 Wb m^{- 2}

. The induced emf across the conductor will be

A wire is bent to form a semicircle of radius a . The wire rotates about its one end with angular velocity ω . Axis of rotation being perpendicular to the plane of the semicircle. In the space, a uniform magnetic field of induction B exists along the axis of rotation, as shown in figure. Then

Important Questions on Electromagnetic Induction

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