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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Important Questions on Electromagnetic Induction

HARD

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

A conducting loop in the shape of right angled isosceles triangle of height

10 cm

is kept such that the

90^{o}

vertex is very close to an infinitely long conducting wire (see the figure). The wire is electrically insulated from the loop. The hypotenuse of the triangle is parallel to the wire. The current in the triangular loop is in counterclockwise direction and increased at constant rate of

10 A s^{- 1} .

Which of the following statement(s) is (are) true?
Question Image

MEDIUM

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:

MEDIUM

Physics>Electricity and Magnetism>Electromagnetic Induction>Production of Induced 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:
Question Image

EASY

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

The magnetic flux through a coil varies with time as

ϕ = 5 t^{2} + 6 t + 9

. The ratio of emf at

t = 3 s

t = 0 s

will be

EASY

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

EASY

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

A conducting circular loop is placed in a uniform magnetic field,

B = 0.025 T

with its plane perpendicular to the loop. The radius of the loop is made to shrink at a constant rate of

1 mm s^{- 1}

. The induced emf when the radius is

2 cm

, is

HARD

Physics>Electricity and Magnetism>Electromagnetic Induction>Production of Induced 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:
Question Image

EASY

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

A metal disc of radius

a = 10 cm

rotates with a constant angular speed of

ω = 200 rad s^{- 1}

about its axis. The potential difference between the centre and the rim of the disc under a uniform magnetic field

B = 5 m T

directed perpendicular to the disc, is

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:

HARD

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

Question Image

HARD

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

Question Image

The figure shows a circular area of tthe radius $R$ where a uniform magnetic field $\vec{B}$ is going into the plane of the paper and increasing in magnitude at a constant rate. In that case, which of the following graphs, drawn schematically, correctly shows the variation of the induced electric field $E (r)$ ?

HARD

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

The figure shows the cross section of a cylindrical region of radius $R$ in which the magnetic field points into the page. The magnitude of the field is $1 T$ at time $t = 0$ and it decreases to zero in $20$ seconds.

Question Image

The induced electric field at a distance $r$ from the centre $O$ inside the cylindrical region is given by

MEDIUM

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

Question Image

HARD

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

A light disc made of aluminium (a nonmagnetic material) is kept horizontally and is free to rotate about its axis as shown in the figure. A strong magnet is held vertically at a point above the disc away from its axis. On revolving the magnet about the axis of the disc, the disc will (figure is schematic and not drawn to scale)

Question Image

EASY

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

MEDIUM

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

A conducting square loop is placed in a magnetic field

B

with its plane perpendicular to the field. The sides of the loop start shrinking at a constant rate

α

. The induced emf in the loop at an instant when its side is

a

HARD

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

A wire loop enclosing a semi-circle of radius $R$ is located on the boundary of a uniform magnetic field of induction $\vec{B} .$ At time $t = 0$ , the loop is set into rotation with velocity $ω$ ? about its axis $0$ , coinciding with a line of vector $\vec{B}$ on the boundary as shown in the figure. The emf induced in the loop is

Question Image

HARD

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

EASY

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

The circular wire in figure below encircles solenoid in which the magnetic flux is increasing at a constant rate out of the plane of the page.

Question Image

The clockwise emf around the circular loop is $ε_{0} .$ By definition a voltammeter measures the voltage difference between the two points given
by $V_{b} - V_{a} = - \int_{a}^{b} \vec{E} \cdot d \vec{s} .$ We assume that $a$ and $b$ are infinitesimally close to each other. The values of $V_{b} - V_{a}$ along the path $1$ and $V_{a} - V_{b}$ along the path $2,$ respectively are

What does flux mean in physics?

Important Questions on Electromagnetic Induction

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