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

HARD

Earn 100

A rectangular loop is moving perpendicular to a non-uniform magnetic field with constant velocity. Find out the expression for induced emf and current and also prove that the law of conservation of energy holds good here.

Important Questions on Electromagnetic Induction

MEDIUM

Physics>Electricity and Magnetism>Electromagnetic Induction>Motional Electromotive Force

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

MEDIUM

Physics>Electricity and Magnetism>Electromagnetic Induction>Motional Electromotive Force

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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EASY

Physics>Electricity and Magnetism>Electromagnetic Induction>Motional Electromotive Force

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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EASY

Physics>Electricity and Magnetism>Electromagnetic Induction>Motional Electromotive Force

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

HARD

Physics>Electricity and Magnetism>Electromagnetic Induction>Motional Electromotive Force

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 Electromotive Force

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

Question Image

MEDIUM

Physics>Electricity and Magnetism>Electromagnetic Induction>Motional Electromotive Force

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:
Question Image

MEDIUM

Physics>Electricity and Magnetism>Electromagnetic Induction>Motional Electromotive Force

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

HARD

Physics>Electricity and Magnetism>Electromagnetic Induction>Motional Electromotive Force

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 :

HARD

Physics>Electricity and Magnetism>Electromagnetic Induction>Motional Electromotive Force

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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EASY

Physics>Electricity and Magnetism>Electromagnetic Induction>Motional Electromotive Force

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?

MEDIUM

Physics>Electricity and Magnetism>Electromagnetic Induction>Motional Electromotive Force

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

HARD

Physics>Electricity and Magnetism>Electromagnetic Induction>Motional Electromotive Force

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 Electromotive Force

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 Electromotive Force

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

Question Image

EASY

Physics>Electricity and Magnetism>Electromagnetic Induction>Motional Electromotive Force

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 Electromotive Force

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 Electromotive Force

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]

Question Image

HARD

Physics>Electricity and Magnetism>Electromagnetic Induction>Motional Electromotive Force

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

Question Image

EASY

Physics>Electricity and Magnetism>Electromagnetic Induction>Motional Electromotive Force

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:

A rectangular loop is moving perpendicular to a non-uniform magnetic field with constant velocity. Find out the expression for induced emf and current and also prove that the law of conservation of energy holds good here.

Important Questions on Electromagnetic Induction

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