In a certain region static electric and magnetic fields exist. The magnetic field is given by B → = B 0 i ^ + 2 j ^ - 4 k ^ . If a test charge moving with a velocity v → = v 0 3 i ^ - j ^ + 2 k ^ experiences no force in that region, then the electric field in the region, in SI units, is:

E → = - v 0 B 0 14 j ^ + 7 k ^

E → = - v 0 B 0 i ^ + j ^ + 7 k ^

E → = - υ 0 B 0 3 i ^ - 2 j ^ - 4 k ^

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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Important Questions on Magnetic Effects of Current and Magnetism

MEDIUM

Physics>Electricity and Magnetism>Magnetic Effects of Current and Magnetism>Magnetic Field

An electron is moving in a circular path under the influence of a transverse magnetic field of

3.57 \times 10^{- 2} T

. If, the value of

\frac{e}{m}

1 .76 \times 10^{11} C {kg}^{- 1}

, the frequency of revolution of the electron is

EASY

Physics>Electricity and Magnetism>Magnetic Effects of Current and Magnetism>Magnetic Field

A proton and an alpha particle both enter a region of uniform magnetic field B, moving at right angles to the field B. if the radius of circular orbits for both the particles is equal and the kinetic energy acquired by proton is 1 MeV, the energy acquired by the alpha particle will be:

HARD

Physics>Electricity and Magnetism>Magnetic Effects of Current and Magnetism>Magnetic Field

If one were to apply the Bohr model to a particle of mass

' m'

and charge

' q'

moving in a plane under the influence of a magnetic field 'B', the energy of the charged particle in the

n^{t h}

level will be:

EASY

Physics>Electricity and Magnetism>Magnetic Effects of Current and Magnetism>Magnetic Field

A negative test charge is moving near a long straight wire carrying a current. The force acting on the test charge is parallel to the direction of the current. The motion of the charge is:

MEDIUM

Physics>Electricity and Magnetism>Magnetic Effects of Current and Magnetism>Magnetic Field

A bar magnet of magnetic moment $M$ is placed at a distance $D$ with its axis along positive $X$ -axis. Likewise, second bar magnet of magnetic moment $M$ is placed at a distance $2 D$ on positive $Y$ -axis and perpendicular to it as shown in the figure. The magnitude of magnetic field at the origin is $|\vec{B}| = α [\frac{μ_{0}}{4 π} \frac{M}{D^{3}}]$ . The value of $α$ must be (Assume $D > >$ where $l$ is the length of magnets)

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MEDIUM

Physics>Electricity and Magnetism>Magnetic Effects of Current and Magnetism>Magnetic Field

In a certain region static electric and magnetic fields exist. The magnetic field is given by

\vec{B} = B_{0} (\hat{i} + 2 \hat{j} - 4 \hat{k})

. If a test charge moving with a velocity

\vec{v} = v_{0} (3 \hat{i} - \hat{j} + 2 \hat{k})

experiences no force in that region, then the electric field in the region, in SI units, is:

MEDIUM

Physics>Electricity and Magnetism>Magnetic Effects of Current and Magnetism>Magnetic Field

A proton (mass $m$ ) accelerated by a potential difference $V$ flies through a uniform transverse magnetic field $B$ . The field occupies a region of space by width $d$ . If $α$ be the angle of deviation of proton from the initial direction of motion (see figure), the value of $\sin α$ will be:
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HARD

Physics>Electricity and Magnetism>Magnetic Effects of Current and Magnetism>Magnetic Field

A charged particle is introduced at the origin

x = 0, y = 0, z = 0

with a given initial velocity

\vec{v}

. A uniform electric field

\vec{E}

and a uniform magnetic field

\vec{B}

exist everywhere. The velocity

\vec{v}

, electric field

\vec{E}

and a uniform magnetic field

\vec{B}

are given in the columns below

Column 1	Column 2	Column 3
1. Electron with $\vec{v} = 2 \frac{E_{0}}{B_{0}} \hat{x}$	(i) $\vec{E} = E_{0} \hat{z}$	(P) $\vec{B} = - B_{0} \hat{x}$
2. Electron with $\vec{v} = \frac{E_{0}}{B_{0}} \hat{y}$	(ii) $\vec{E} = - E_{0} \hat{y}$	(Q) $\vec{B} = B_{0} \hat{x}$
3.Proton with $\vec{v} = 0$	(iii) $\vec{E} = {- E}_{0} \hat{x}$	(R) $\vec{B} = B_{0} \hat{y}$
4. Proton with $\vec{v} = 2 \frac{E_{0}}{B_{0}} \hat{x}$	(iv) $\vec{E} = E_{0} \hat{x}$	(S) $\vec{B} = B_{0} \hat{z}$

In which case will the particle describe a helical path with axis along positive z direction?

MEDIUM

Physics>Electricity and Magnetism>Magnetic Effects of Current and Magnetism>Magnetic Field

The ratio of magnetic fields due to a bar magnet at the two axial points

P_{1}

and

P_{2}

which are separated from each other by

10 cm

25 : 2

P_{1}

Point is situated at

10 cm

from the centre of the magnet. (Points

P_{1}

and

P_{2}

are on the same side of magnet and distance of

P_{1}

and

P_{2}

from the centre of magnet is much greater than the distance of two ends of the magnet from the centre). Magnetic length of the bar magnet is

MEDIUM

Physics>Electricity and Magnetism>Magnetic Effects of Current and Magnetism>Magnetic Field

A proton and an

α

- particle (with their masses in the ratio of

1 : 4

and charges in the ratio of

1 : 2

) are accelerated from rest through a potential difference

V .

If a uniform magnetic field

(B)

is set up perpendicular to their velocities, the ratio of the radii

r_{p} : r_{α}

of the circular paths described by them will be:

MEDIUM

Physics>Electricity and Magnetism>Magnetic Effects of Current and Magnetism>Magnetic Field

An electron, a proton and an alpha particle having the same kinetic energy are moving in circular orbits of radii

r_{e}, r_{p}, r_{α}

respectively in a uniform magnetic field B. The relation between

r_{e}, r_{p}, r_{α}

is:

MEDIUM

Physics>Electricity and Magnetism>Magnetic Effects of Current and Magnetism>Magnetic Field

The magnetic field of earth at the equator is approximately

4 \times 1 0^{- 5} T

. The radius of earth is

6.4 \times 1 0^{6} m

. Then the dipole moment of the earth will be nearly of the order of :

EASY

Physics>Electricity and Magnetism>Magnetic Effects of Current and Magnetism>Magnetic Field

A proton, a deuteron and an

α

-particle with same kinetic energy enter into a uniform magnetic field at right angle to magnetic field. The ratio of the radii of their respective circular paths is :

HARD

Physics>Electricity and Magnetism>Magnetic Effects of Current and Magnetism>Magnetic Field

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)

HARD

Physics>Electricity and Magnetism>Magnetic Effects of Current and Magnetism>Magnetic Field

A charged particle is introduced at the origin

x = 0, y = 0, z = 0

with a given initial velocity

\vec{v}

. A uniform electric field

\vec{E}

and a uniform magnetic field

\vec{B}

exist everywhere. The velocity

\vec{v}

, electric field

\vec{E}

and a uniform magnetic field

\vec{B}

are given in the columns below

Column 1	Column 2	Column 3
1. Electron with $\vec{v} = 2 \frac{E_{0}}{B_{0}} \hat{x}$	(i) $\vec{E} = E_{0} \hat{z}$	(P) $\vec{B} = - B_{0} \hat{x}$
2. Electron with $\vec{v} = \frac{E_{0}}{B_{0}} \hat{y}$	(ii) $\vec{E} = - E_{0} \hat{y}$	(Q) $\vec{B} = B_{0} \hat{x}$
3.Proton with $\vec{v} = 0$	(iii) $\vec{E} = {- E}_{0} \hat{x}$	(R) $\vec{B} = B_{0} \hat{y}$
4. Proton with $\vec{v} = 2 \frac{E_{0}}{B_{0}} \hat{x}$	(iv) $\vec{E} = E_{0} \hat{x}$	(S) $\vec{B} = B_{0} \hat{z}$

In which case will the particle move in a straight line with a constant velocity?

HARD

Physics>Electricity and Magnetism>Magnetic Effects of Current and Magnetism>Magnetic Field

A uniform magnetic field

B

exists in the region between

x = 0

and

x = \frac{3 R}{2}

(region

2

in the figure) pointing normally into the plane of the paper. A particle with charge

+ Q

and momentum

p

directed along

x

-axis enters region

2

from region

1

at point

P_{1} (y = - R) .

Which of the following option(s) is/are correct?

Question Image

HARD

Physics>Electricity and Magnetism>Magnetic Effects of Current and Magnetism>Magnetic Field

A charged particle is introduced at the origin

x = 0, y = 0, z = 0

with a given initial velocity

\vec{v}

. A uniform electric field

\vec{E}

and a uniform magnetic field

\vec{B}

exist everywhere. The velocity

\vec{v}

, electric field

\vec{E}

and a uniform magnetic field

\vec{B}

are given in the columns below

Column 1	Column 2	Column 3
1. Electron with $\vec{v} = 2 \frac{E_{0}}{B_{0}} \hat{x}$	(i) $\vec{E} = E_{0} \hat{z}$	(P) $\vec{B} = - B_{0} \hat{x}$
2. Electron with $\vec{v} = \frac{E_{0}}{B_{0}} \hat{y}$	(ii) $\vec{E} = - E_{0} \hat{y}$	(Q) $\vec{B} = B_{0} \hat{x}$
3.Proton with $\vec{v} = 0$	(iii) $\vec{E} = {- E}_{0} \hat{x}$	(R) $\vec{B} = B_{0} \hat{y}$
4. Proton with $\vec{v} = 2 \frac{E_{0}}{B_{0}} \hat{x}$	(iv) $\vec{E} = E_{0} \hat{x}$	(S) $\vec{B} = B_{0} \hat{z}$

In which case would the particle move in a straight line along the negative direction of y axis

HARD

Physics>Electricity and Magnetism>Magnetic Effects of Current and Magnetism>Magnetic Field

In the

xy - plane

, the region

y > 0

has a uniform magnetic field

B_{1} \hat{k}

and the region

y < 0

has another uniform magnetic field

B_{2} \hat{k}

. A positively charged particle is projected from the origin along the positive

y - axis

with speed

v_{0} = π m s^{- 1}

t = 0

, as shown in the figure. Neglect gravity in this problem. Let

t = T

be the time when the particle crosses the

x - axis

from below for the first time. If

B_{2} = 4 B_{1}

, the average speed of the particle, in

m s^{- 1}

, along the

x - axis

in the time interval

T

is ________.

Question Image

HARD

Physics>Electricity and Magnetism>Magnetic Effects of Current and Magnetism>Magnetic Field

Two short bar magnets

A

and

B

(having magnetic moments

M_{1}

and

M_{2}

respectively) are kept one above the other with their magnetic axis perpendicular to each other. If their resultant at a point on the axis of magnet

A

is inclined at

45 °

with the axis of magnet

A

then the ratio of magnetic moments

\frac{M_{2}}{M_{1}}

[\tan 45 ° = 1]

EASY

Physics>Electricity and Magnetism>Magnetic Effects of Current and Magnetism>Magnetic Field

A magnetic field cannot

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Important Questions on Magnetic Effects of Current and Magnetism

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