Moving Charges and Magnetism

part 1

Magnetic Force

• Concept of magnetic field
• Oersted's experiment
• Motion of charge in magnetic field
• Velocity selector and cyclotron
• Force on a current-carrying conductor

part 2

Biot-Savart Law and Ampere's Law

• Biot-Savart law
• Magnetic field due to a straight wire
• Magnetic field on axis of circular loop
• Ampere's circuital law
• Magnetic field due to solenoid and toroid

part 3

Force Between Conductors and Galvanometer

• Force between two parallel conductors
• Definition of ampere
• Torque on a rectangular loop
• Moving coil galvanometer
• Conversion to ammeter and voltmeter

Biot-Savart law

$dB = \frac{\mu_0}{4\pi} \cdot \frac{I\,dl\sin\theta}{r^2}$

★ board favourite

B at centre of circular loop

$B = \frac{\mu_0 I}{2R}$

★ board favourite

Ampere's circuital law

$\oint \vec{B}\cdot d\vec{l} = \mu_0 I_{enc}$

★ board favourite

B inside solenoid

$B = \mu_0 nI$ (n = N/L turns/metre)

★ board favourite

B due to long straight wire

$B = \frac{\mu_0 I}{2\pi r}$

★ board favourite

Lorentz force on moving charge

$F = q(\vec{v}\times\vec{B})$; $F = qvB\sin\theta$

★ board favourite

Force on current-carrying conductor

$F = BIL\sin\theta$; $\vec{F} = I\vec{L}\times\vec{B}$

★ board favourite

B on axis of circular loop

$B = \frac{\mu_0 I R^2}{2(R^2+x^2)^{3/2}}$

★ frequently asked

B inside toroid

$B = \frac{\mu_0 NI}{2\pi r}$

★ frequently asked

Force per unit length between two wires

$\frac{F}{L} = \frac{\mu_0 I_1 I_2}{2\pi d}$

★ frequently asked

Draw a labelled diagram of a cyclotron and explain its working principle. Derive an expression for the cyclotron frequency. Why cannot a cyclotron accelerate electrons?

Two long parallel straight wires carry currents I₁ and I₂ in the same direction. Derive the expression for the force per unit length between them and state whether it is attractive or repulsive.

State Biot-Savart law. Using it, derive the expression for the magnetic field at the centre of a circular current loop. Hence write the magnetic field at the centre of a semicircular current loop.

A charged particle of charge q and mass m enters a uniform magnetic field B perpendicular to its velocity v. Derive the expression for the radius of its circular path and its time period. Show that the time period is independent of the speed.

State Ampere's circuital law. Use it to find the magnetic field inside a solenoid of n turns per unit length carrying current I.

Write the expression for the Lorentz force experienced by a charge q moving with velocity v in the presence of both electric field E and magnetic field B.

A proton moves with velocity v along the axis of a solenoid. What is the force on the proton due to the magnetic field of the solenoid?

Derive an expression for the torque acting on a rectangular current-carrying loop placed in a uniform magnetic field. Hence define the magnetic moment of the loop.

Explain the working principle of a moving coil galvanometer. How is it converted into (a) an ammeter, (b) a voltmeter?

A charged particle moves undeflected through a region of space. If the electric field is E and the magnetic field is B, what is the speed of the particle?

State Ampere's circuital law. Using it, derive the expression for the magnetic field due to a toroidal solenoid. How does the field inside the toroid compare with that outside it?

Write Biot-Savart law in vector form. Use it to state the direction of the magnetic field at a point due to a small current element.

How many marks is Moving Charges and Magnetism worth in the Class 12 board exam?

Around 6 marks of the 70-mark CBSE Physics theory paper, based on the official unit-wise weightage. Biot-Savart & Ampere's law — practice derivations.

Is Moving Charges and Magnetism easy or hard?

It's rated hard — one of the tougher chapters in Class 12 Physics. Most students need about 5 hours to cover it well.

What are the important topics in Moving Charges and Magnetism?

The chapter covers 15 NCERT topics in 3 areas: Magnetic Force; Biot-Savart Law and Ampere's Law; Force Between Conductors and Galvanometer.

What questions come from Moving Charges and Magnetism in board exams?

Between 2018–2024, CBSE board papers asked questions from this chapter on Cyclotron, Force between Conductors, Biot-Savart Law, Magnetic Force — 1- to 5-mark questions.