Moving Charges And Magnetism

Previous Years' CBSE Board Questions

4.2 Magnetic Force

Force on a Charged Particle in a Uniform Magnetic Field

/SA (1 mark)

1. Write the expression, in a vector form, for the Lorentz magnetic force <math>\vec{F}</math> due to a charge moving with velocity v in a magnetic field B. What is the direction of the magnetic force? (Delhi 2014) R
2. Define one tesla using the expression for the magnetic force acting on a particle of charge 'q' moving with velocity ♥ in a magnetic field B.

(Foreign 2014) R

Force on a Current Carrying Conductor in a Uniform Magnetic Field

A charge particle after being accelerated through a

potential difference 'V' enters in a uniform magnetic

field and moves in a circle of radius r. If V is doubled,

the radius of the circle will become

1. 2r (b) √2r
2. 41 (d) r/√2 (2020)

Two particles of masses <math>m_1</math> and <math>m_2</math> have equal

charges. They are accelerated from rest through a

potential difference V and then enter in a region of

uniform magnetic field <math>\vec{B}</math>. If they describe circular

paths of radii r₁ and r₂, respectively, then the value

of <math>m_1/m_2</math> is

<math>\left(\frac{\mathbf{r}_2}{\mathbf{r}_1}\right)^2</math> (b) <math>\frac{r_1V}{r_2B}</math> (c) <math>\left(\frac{r_1}{r_2}\right)^2</math> (d) <math>\frac{r_1^2V}{r_2^2B}</math>

(AI 2020C) VSA (1 mark)

MCQ

1. A straight conducting rod of length <math>\ell</math> and mass m is suspended in a horizontal plane by a pair of flexible strings in a magnetic field of magnitude B. To remove the tension in the supporting strings, the magnitude of the current in the wire is

(a)

(b) <math>\frac{mg\ell}{B}</math> (c) <math>\frac{mg}{\ell B}</math> (d)

(Term I 2021-22) R

1. A current carrying wire kept in a uniform magnetic field will experience a maximum force when it is
2. perpendicular to the magnetic field
3. parallel to the magnetic field
4. at an angle of 45° to the magnetic field

(2018)

1. at an angle of 60° to the magnetic field

(Term I 2021-22) R

SAI (2 marks)

1. A straight wire of mass 200 g and length 1.5 m carries a current of 2 A. It is suspended in mid air by a uniform magnetic field B. What is the magnitude of the magnetic field? (2/3, Foreign 2015) R

4.3 Motion in a Magnetic Field

MCQ

A particle of mass m and charge -q is moving with a uniform speed v in a circle of radius r, with another charge q at the centre of the circle. The value of r is (a) <math>\frac{1}{4\pi\epsilon_0 m} \left(\frac{q}{v}\right)</math>

1. <math>\frac{1}{4\pi\epsilon_0 m} \left(\frac{q}{v}\right)^2</math>
2. (d) <math>\frac{m}{4\pi\epsilon_0} \left(\frac{q}{v}\right)^2</math> (2023)

<math>\frac{m}{4\pi\epsilon_0} \left(\frac{q}{v}\right)</math>

Compare

1. their kinetic energies, and
2. if the radius of the circular path described by proton is 5 cm, determine the radii of the path described by deuteron and alpha particle.

(Al 2019)

1. (a) A particle of charge 'q' and mass 'm', moving with velocity 'v' is subjected to a uniform magnetic field B perpendicular to its velocity. Show that the particle describes a circular path. Obtain expression for the radius of the circular path of the particle.

1. Explain, how its path will be affected if the velocity v makes an angle θ (# 90°) with the direction of the magnetic field. (Al 2019C)
2. An electron moves along +x direction. It enters into a region of uniform magnetic field B directed along-z direction 35 shown in figure. Draw the shape of trajectory followed by the electron after entering the field.

(2020)

1. A proton and an electron travelling along parallel paths enter a region of uniform magnetic field, acting perpendicular to their paths. Which of them will move in a circular path with higher frequency?
2. A particle of mass 'm' and charge 'q' moving with velocity 'v' enters the region of uniform magnetic field at right angle to the direction of its motion. How does its kinetic energy get affected?

(Delhi 2015C)

SAI (2 marks)

A charged particle q is moving in the presence of

a magnetic field B which is inclined to an angle 30°

with the direction of the motion of the particle.

Draw the trajectory followed by the particle in the

presence of the field and explain how the particle

describes this path. (Delhi 2019) An

SAII (3 marks)

A proton, a deuteron and an alpha particle are

accelerated through the same potential difference

and then subjected to a uniform magnetic field <math>\bar{B}</math>,

perpendicular to the direction of their motions.

Deduce an expression for the frequency of

revolution of a charged particle in a magnetic field

and show that it is independent of velocity or energy

of the particle. (Al 2014)

LΑ (5 marks)

20. An α-particle is accelerated through a potential

difference of 10 kV and moves along x-axis. It enters

in a region of uniform magnetic field B = <math>2 \times 10^{-3}</math> T

acting along y-axis. Find the radius of its path.

(Take mass of <math>\alpha</math>-particle = <math>6.4 \times 10^{-27}</math> kg)

(2/5, 2020)

Motion in Combined Electric and Magnetic Fields