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.

HARD

Earn 100

Mention the different fields used in the velocity selector.

Important Questions on Moving Charges and Magnetism

MEDIUM

Physics>Electricity and Magnetism>Moving Charges and Magnetism>Motion in Combined Electric and Magnetic Fields

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>Moving Charges and Magnetism>Motion in Combined Electric and Magnetic Fields

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>Moving Charges and Magnetism>Motion in Combined Electric and Magnetic Fields

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>Moving Charges and Magnetism>Motion in Combined Electric and Magnetic Fields

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>Moving Charges and Magnetism>Motion in Combined Electric and Magnetic Fields

A velocity selector consists of electric field $\vec{E} = E \hat{k}$ and magnetic field $\vec{B} = B \hat{j}$ with $B = 12 mT$ . The value $E$ required for an electron of energy $728 eV$ moving along the positive $x$ -axis to pass undeflected is

(Given, mass of electron $= 9.1 \times 10^{- 31} kg$ )

MEDIUM

Physics>Electricity and Magnetism>Moving Charges and Magnetism>Motion in Combined Electric and Magnetic Fields

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>Moving Charges and Magnetism>Motion in Combined Electric and Magnetic Fields

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:
Question Image

HARD

Physics>Electricity and Magnetism>Moving Charges and Magnetism>Motion in Combined Electric and Magnetic Fields

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?

MEDIUM

Physics>Electricity and Magnetism>Moving Charges and Magnetism>Motion in Combined Electric and Magnetic Fields

At a place, an electric field and a magnetic field are in the downward direction. There an electron moves in the downward direction. Hence this electron.____________.

MEDIUM

Physics>Electricity and Magnetism>Moving Charges and Magnetism>Motion in Combined Electric and Magnetic Fields

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>Moving Charges and Magnetism>Motion in Combined Electric and Magnetic Fields

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>Moving Charges and Magnetism>Motion in Combined Electric and Magnetic Fields

In a region, an electric field $\vec{E} = 5 x^{3} \hat{j} {NC}^{- 1}$ and a magnetic field of $\vec{B} = 0.1 \hat{k} T$ are applied. A beam of positively charged particles is projected along X-direction. Find the velocity of particles that move undeflected in these crossed fields.

EASY

Physics>Electricity and Magnetism>Moving Charges and Magnetism>Motion in Combined Electric and Magnetic Fields

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>Moving Charges and Magnetism>Motion in Combined Electric and Magnetic Fields

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>Moving Charges and Magnetism>Motion in Combined Electric and Magnetic Fields

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>Moving Charges and Magnetism>Motion in Combined Electric and Magnetic Fields

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>Moving Charges and Magnetism>Motion in Combined Electric and Magnetic Fields

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?

HARD

Physics>Electricity and Magnetism>Moving Charges and Magnetism>Motion in Combined Electric and Magnetic Fields

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

MEDIUM

Physics>Electricity and Magnetism>Moving Charges and Magnetism>Motion in Combined Electric and Magnetic Fields

Obtained the formula for Lorentz force on a moving electric charge in a uniform electric and magnetic field.

EASY

Physics>Electricity and Magnetism>Moving Charges and Magnetism>Motion in Combined Electric and Magnetic Fields

A charged particles of mass

m

and charge

q

moves along a circular path of radius

r

that is perpendicular to a magnetic field

B

. The time taken by the particle to complete one revolution is

Mention the different fields used in the velocity selector.

Important Questions on Moving Charges and Magnetism

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