Two infinitely long straight wires lie in the xy - plane along the lines x = ± R . The wire located at x = + R carries a constant current I 1 and the wire located at x = - R carries a constant current I 2 . A circular loop of radius R is suspended with its centre at 0 , 0 3 R and in a plane parallel to the xy - plane. This loop carries a constant current I in the clockwise direction as seen from above the loop. The current in the wire is taken to be positive if it is in the + j ^ direction. Which of the following statements regarding the magnetic field B → is (are) true?

If I 1 = I 2 , Then the z - component of the magnetic field at the centre of the loop is - μ 0 I 2 R

If I 1 < 0 a n d I 2 > 0 , t h e n B → can be equal to zero at the origin 0 , 0 , 0

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

A particle of mass M and positive charge Q , moving with a constant velocity u → 1 = 4 i ^ m s - 1 , enters a region of uniform static magnetic field normal to the x - y plane. The region of the magnetic field extends from x = 0 to x = L for all values of y . After passing through this region, the particle emerges on the other side after 10 milliseconds with a velocity u → 2 = 2 3 i ^ + j ^ m s - 1 . The correct statement (s) is (are)

The magnitude of the magnetic field 5 0 π M 3 Q units.

The direction of the magnetic field is +z direction.

The magnitude of the magnetic field 1 0 0 π M 3 Q units.

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The following statement is false for Helmholtz coils:

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Important Questions on Magnetic Effect of Current

HARD

Physics>Electricity and Magnetism>Magnetic Effect of Current>Helmholtz Coils

A rectangular loop of sides $10 cm$ and $5 cm$ , carrying a current $I$ of $12 A$ , is placed in different orientations as shown in the figure below.
(a) Question Image (b)

(c) (d)

If there is a uniform magnetic field of $0.3 T$ in the positive $z$ direction, in which orientations the loop would be in $(i)$ stable equilibrium and $(ii)$ unstable equilibrium?

HARD

Physics>Electricity and Magnetism>Magnetic Effect of Current>Helmholtz Coils

A small circular loop of conducting wire has radius a and carries current

I .

It is placed in a uniform magnetic field

B

perpendicular to its plane such that when rotated slightly about its diameter and released, it starts performing simple harmonic motion of time period

T .

The mass of the loop is

m

then:

EASY

Physics>Electricity and Magnetism>Magnetic Effect of Current>Helmholtz Coils

A circular current loop of magnetic moment

M

is in an arbitrary orientation in an external uniform magnetic field

\vec{B}

. The work done to rotate the loop by

30 °

about an axis perpendicular to its plane is

MEDIUM

Physics>Electricity and Magnetism>Magnetic Effect of Current>Helmholtz Coils

A magnet of total magnetic moment

10^{- 2} \hat{i} A m^{2}

is placed in a time varying magnetic field,

B \hat{i} (\cos ω t)

where

B = 1

Tesla and

ω = 0.125 rad s^{- 1}

. The work done for reversing the direction of the magnetic moment at

t = 1

second, is:

MEDIUM

Physics>Electricity and Magnetism>Magnetic Effect of Current>Helmholtz Coils

Two infinitely long straight wires lie in the xy - plane along the lines

x = \pm R

. The wire located at

x = + R

carries a constant current

I_{1}

and the wire located at

x = - R

carries a constant current

I_{2}

. A circular loop of radius R is suspended with its centre at

(0, 0 \sqrt{3} R)

and in a plane parallel to the xy - plane. This loop carries a constant current

I

in the clockwise direction as seen from above the loop. The current in the wire is taken to be positive if it is in the

+ \hat{j}

direction. Which of the following statements regarding the magnetic field

\vec{B}

is (are) true?

MEDIUM

Physics>Electricity and Magnetism>Magnetic Effect of Current>Helmholtz Coils

A coil in the shape of an equilateral triangle of side

l

is suspended between the pole pieces of a permanent magnet such that

B

is in plane of the coil. If due to a current

i

in the triangle, a torque

τ

rests on it, the side

l

of the triangle is

MEDIUM

Physics>Electricity and Magnetism>Magnetic Effect of Current>Helmholtz Coils

A magnetic needle has a magnetic moment of

5 \times 10^{- 2} {Am}^{2}

and moment of inertia

8 \times 10^{- 6} {kgm}^{2}

. It has a period of oscillation of

2 s

in a magnetic field

\vec{B}

. The magnitude of magnetic field is approximately;

HARD

Physics>Electricity and Magnetism>Magnetic Effect of Current>Helmholtz Coils

In a uniform magnetic field, the magnetic needle has a magnetic moment

9.85 \times 10^{- 2} A m^{- 2}

and moment of inertia

5 \times 10^{- 6} kg m^{2} .

If it performs

10

complete oscillations in

5

seconds then the magnitude of the magnetic field is ____

mT

[Take

π^{2}

9.85]

EASY

Physics>Electricity and Magnetism>Magnetic Effect of Current>Helmholtz Coils

A magnetic dipole in a uniform magnetic field has: (Take zero potential energy when magnetic dipole is perpendicular to magnetic field)

EASY

Physics>Electricity and Magnetism>Magnetic Effect of Current>Helmholtz Coils

A magnetic dipole is acted upon by two magnetic fields which are inclined to each other at an angle of

75^{o}

. One of the fields has a magnitude of

15 mT

. The dipole attains stable equilibrium at an angle of

30^{o}

with this field. The magnitude of the other field (in

mT

) is close to

EASY

Physics>Electricity and Magnetism>Magnetic Effect of Current>Helmholtz Coils

A bar magnet of magnetic moment

5 A m^{2}

is placed in a uniform magnetic induction

3 \times 10^{- 5} T .

If each pole of a magnet experiences a force of

2.5 \times 10^{- 4} N

then the magnetic length of the magnet is

MEDIUM

Physics>Electricity and Magnetism>Magnetic Effect of Current>Helmholtz Coils

A rectangular coil of length

0.12 m

and width

0.1 m

having

50

turns of wire is suspended vertically in a uniform magnetic field of strength

0.2

W e b e r / m^{2}

. The coil carries a current of

2 A

. If the plane of the coil is inclined at an angle of

30^{o}

with the direction of the field, the torque required to keep coil in stable equilibrium will be:

EASY

Physics>Electricity and Magnetism>Magnetic Effect of Current>Helmholtz Coils

A magnetic dipole of moment

\vec{m}

is placed in the magnetic field

\vec{B}

. It is free to rotate about an axis about which its moment of inertia is

I

. It is displaced by a small angle

θ_{0} (θ_{0} < < 1)

at time

t = 0 s

and released. The dipole undergoes simple harmonic motion with angular frequency

ω

. Its potential energy at time

t

is : (Assume

\sin (α) \approx α, \cos (α) \approx 1 - \frac{α^{2}}{2}

α < < 1

)

MEDIUM

Physics>Electricity and Magnetism>Magnetic Effect of Current>Helmholtz Coils

A circular coil has moment of inertia

0.8 kg m^{2}

around any diameter and is carrying current to produce a magnetic moment of

20 A m^{2}

. The coil is kept initially in a vertical position and it can rotate freely around a horizontal diameter. When a uniform magnetic field of

4 T

is applied along the vertical, it starts rotating around its horizontal diameter. The angular speed the coil acquires after rotating by

60^{o}

will be :

EASY

Physics>Electricity and Magnetism>Magnetic Effect of Current>Helmholtz Coils

A bar magnet is held perpendicular to uniform magnetic field. The torque acting on the magnet is to be made half by rotating it. It should be rotated through an angle

(\sin 30 ° = 0.5, \sin 90 ° = 1)

MEDIUM

Physics>Electricity and Magnetism>Magnetic Effect of Current>Helmholtz Coils

Two short magnetic dipoles $m_{1}$ and $m_{2}$ each having magnetic moment of $1 A m^{2}$ are placed at point $O$ and $P$ respectively. The distance between $O P$ is $1 m$ . The torque experienced by the magnetic dipole $m_{2}$ due to the presence of $m_{1}$ is $________\times 10^{- 7} N m$ .

Question Image

EASY

Physics>Electricity and Magnetism>Magnetic Effect of Current>Helmholtz Coils

Work done in displacing a Magnetic Dipole of magnetic moment

M

, (Bar Magnet) in Uniform Magnetic Field

B

from an angle

θ_{1}

θ_{2}

HARD

Physics>Electricity and Magnetism>Magnetic Effect of Current>Helmholtz Coils

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>Magnetic Effect of Current>Helmholtz Coils

A particle of mass

M

and positive charge

Q

, moving with a constant velocity

{\vec{u}}_{1} = 4 \hat{i} m s^{- 1}

, enters a region of uniform static magnetic field normal to the

x - y

plane. The region of the magnetic field extends from

x = 0

x = L

for all values of

y

. After passing through this region, the particle emerges on the other side after 10 milliseconds with a velocity

{\vec{u}}_{2} = 2 (\sqrt{3} \hat{i} + \hat{j}) m s^{- 1}

. The correct statement (s) is (are)

MEDIUM

Physics>Electricity and Magnetism>Magnetic Effect of Current>Helmholtz Coils

A bar magnet is hung by a thin cotton thread in a uniform horizontal magnetic field and is in equilibrium state. The energy required to rotate it by

60^{o}

W

. Now, the torque required to keep the magnet in this new position is

The following statement is false for Helmholtz coils:

Important Questions on Magnetic Effect of Current

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