Magnetic Force: Overview, Questions, Preparation

This chapter has multiple topics listed below:

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Dhanya B

Updated on Oct 5, 2023 15:57 IST

Magnetic Force is a fundamental concept related to the interaction of magnets and moving charges in NCERT Class 12 Physics. Understanding magnetic forces is crucial for comprehending various phenomena, including the behaviour of charged particles in magnetic fields and the operation of devices like electric motors and generators.

Table of Contents

Magnetic Field
Magnetic Force on a Moving Charge
Direction of Magnetic Force
Circular Motion of Charged Particles
Applications of Magnetic Force
FAQs on Magnetic Force

Magnetic Field

A magnetic field is a region in space where the influence of a magnet or a moving charge is felt. It exerts a force on other magnets or moving charged particles. Magnetic fields are typically represented by field lines that show the direction of the magnetic force at various points in space.

Magnetic Force on a Moving Charge

When a charged particle, such as an electron or a proton, moves through a magnetic field, it experiences a magnetic force. This force acts perpendicular to both the particle's velocity and the direction of the magnetic field. The following formula gives the magnitude of the magnetic force on the charged particle:

F=qvBsin(θ)

Where:

F is the magnetic force.
q is the charge of the particle.
v is the velocity of the particle.
B is the strength of the magnetic field.
θ is the angle between the velocity vector and the magnetic field direction.

Direction of Magnetic Force

The direction of the magnetic force can be determined using the right-hand rule. If you point your thumb in the direction of the particle's velocity and your fingers in the direction of the magnetic field, then the force experienced by the charge is perpendicular to both and can be found by the direction in which your palm faces.

If the charge is positively charged, the force is in one direction.
If the charge is negatively charged, the force is in the opposite direction.

Circular Motion of Charged Particles

When a charged particle moves in a magnetic field, it experiences a magnetic force that acts as a centripetal force, causing the particle to move in a circular path. The radius of this path is given by the formula:

r= mv/∣q∣B

Where:

r is the radius of the circular path.
m is the mass of the particle.
v is the velocity of the particle.
∣q∣ is the magnitude of the charge.
B is the magnetic field strength.

Applications of Magnetic Force

Magnetic force has numerous practical applications, including:

Electric Motors: Electric motors use magnetic fields to produce mechanical motion by exerting magnetic forces on wires carrying electric currents.
Generators: Generators use mechanical energy to produce electric currents by rotating coils of wire in a magnetic field.
Cathode Ray Tubes (CRTs): In older televisions and computer monitors, CRTs use magnetic deflection to move the electron beam, creating images on the screen.
Particle Accelerators: Devices like cyclotrons and synchrotrons use strong magnetic fields to accelerate charged particles to high speeds.

FAQs on Magnetic Force

Q. What is the magnitude of magnetic force per unit length on a wire carrying a current of 8 A and making an angle of 30º with the direction of a uniform magnetic field of 0.15 T?

Current in the wire, I = 8 A

Magnitude of the uniform magnetic field, B = 0.15 T

Angle between the wire and the magnetic field, = 30

Magnetic force per unit length of the wire is given as

f = BI = 0.15 = 0.6 N/m

Q. Two long and parallel straight wires A and B carrying currents of 8.0 A and 5.0 A in the same direction are separated by a distance of 4.0 cm. Estimate the force on a 10 cm section of wire A.

Current flowing in wire A, = 8.0 A

Current flowing in wire B, = 5.0 A

Distance between two wires, r = 4.0 cm = 0.04 m

Length of the section of the wire A, L = 10 cm = 0.1 m

Force exerted on length L due to magnetic field is given as:

F = , where = permeability of free space = 4 Tm

F = = 2 N

The magnitude of force is 2 N. This is an attractive force normal to A, towards B. Because the direction of the currents in both the wire is same.

Q. In a chamber, a uniform magnetic field of 6.5 G (1 G = 10–4 T) is maintained. An electron is shot into the field with a speed of 4.8 × 106 m s–1 normal to the field. Explain why the path of the electron is a circle. Determine the radius of the circular orbit. (e = 1.6 × 10–19 C, me = 9.1×10–31 kg)

Magnetic field strength, B = 6.5 G = 6.5 T

Speed of electron, v = 4.8 m/s

Charge of electron, e = 1.6 C

Mass of electron, m = 9.1 kg

Angle between the shot electron and the magnetic field, = 90

Magnetic force exerted on the electron in the magnetic field is given as:

F = evB

This force provides centripetal force to the moving electron. Hence, the electron starts moving in a circular path of radius r

The centripetal force exerted on electron, =

In equilibrium, the centripetal force exerted on electron = magnetic force on the electron

F =

evB

r = = = 4.20 m = 4.20 cm

Q. From the previous question obtain the frequency of revolution of the electron in its circular orbit. Does the answer depend on the speed of the electron? Explain.

Let the frequency of revolution =

Angular frequency =

Now, velocity of electron, v = r

Since in circular orbit, magnetic force is balanced by the centripetal force, we can write

evB or eB = = =

This frequency is independent of the speed of electron.

Hz = 18.19 MHz