Last Updated: May 2026
CBSE Class 12 Physics Chapter 4 — Moving Charges and Magnetism overview
For CBSE Class 12 Physics Chapter 4 (Moving Charges and Magnetism), the chapter is high-weight in the board exam (~5-7 marks) and JEE/NEET (3-4 questions). The NCERT chapter develops the magnetic field due to currents (Biot-Savart, Ampere’s law), force on moving charges and currents, and applications (cyclotron, moving-coil galvanometer).
Quick Concept Map
| Section | Key Formula |
|---|---|
| Magnetic force on moving charge | F = qv × B |
| Force on current-carrying wire | F = IL × B |
| Lorentz force | F = q(E + v × B) |
| Biot-Savart law (differential) | dB = (μ₀/4π) (Idl × r̂)/r² |
| Ampere’s law (integral) | ∮B·dl = μ₀Ienc |
| B at centre of circular loop | B = μ₀I/(2R) |
| B on axis of circular loop (distance x) | B = μ₀IR²/[2(R²+x²)3/2] |
| B inside long solenoid | B = μ₀nI |
| B inside toroid | B = μ₀NI/(2πr) |
| Cyclotron frequency | f = qB/(2πm) |
| Cyclotron radius (max) | r = mv/(qB) |
| Magnetic moment of current loop | m = NIA |
| Torque on current loop in B | τ = m × B; |τ| = NIAB sinθ |
1. Magnetic Force on Moving Charge — F = qv × B
The magnetic force is always perpendicular to velocity, so it does no work — only changes direction, not speed. For a charge moving perpendicular to B, motion is circular with radius r = mv/(qB) and angular velocity ω = qB/m.
2. Force on Current-Carrying Wire — F = IL × B
Direction by right-hand rule. For a straight wire of length L in uniform B: F = BIL sinθ. Two parallel wires carrying currents in same direction attract; opposite direction repel. Force per unit length = (μ₀ I₁I₂)/(2πd).
3. Biot-Savart Law
dB = (μ₀/4π) (I dl × r̂)/r²
Direction: by right-hand rule for cross product. Magnitude: dB = (μ₀/4π) (I dl sinθ)/r². Use it to derive B at centre of loop, on axis of loop, etc.
4. Magnetic Field at Centre of Circular Loop
Apply Biot-Savart with sinθ = 90° (since dl is tangent, r is radial). Integrate around the loop:
B = μ₀I/(2R) (at centre); for N turns: B = μ₀NI/(2R).
5. Magnetic Field on Axis of Circular Loop
At distance x along axis from centre of loop of radius R:
B = μ₀IR²/[2(R²+x²)3/2]
Far from loop (x ≫ R): B ≈ μ₀(2m)/(4πx³) where m = IπR² is magnetic moment.
6. Ampere’s Circuital Law
∮ B·dl = μ₀ Ienc
Useful for high-symmetry problems:
- Long straight wire: B = μ₀I/(2πr)
- Long solenoid (inside): B = μ₀nI (where n = turns/length)
- Toroid: B = μ₀NI/(2πr)
7. Cyclotron
Device to accelerate charged particles using electric field (between dees) and magnetic field (perpendicular to dees). Charge moves in semicircular path in each dee, gaining energy at the gap each half-cycle.
- Cyclotron frequency: f = qB/(2πm) — independent of velocity (non-relativistic)
- Maximum kinetic energy: KEmax = q²B²r²/(2m)
- Cannot accelerate electrons (relativistic effect at high speed); cannot accelerate neutrons (no charge)
8. Magnetic Moment and Torque
- Magnetic moment: m = NIA n̂
- Torque in uniform field: τ = m × B
- Potential energy: U = −m·B
- Stable equilibrium: when m parallel to B (U = −mB)
- Unstable equilibrium: when m antiparallel to B (U = +mB)
9. Moving-Coil Galvanometer (MCG)
A current-carrying coil in a magnetic field experiences torque, balanced by spring restoring torque. Deflection angle φ is proportional to current:
- φ = (NAB/k) I, where k = spring constant
- Current sensitivity: φ/I = NAB/k
- Voltage sensitivity: φ/V = NAB/(kR), where R is coil resistance
- Conversion to ammeter: shunt low resistance in parallel
- Conversion to voltmeter: high resistance in series
20 Important Board-Pattern Questions
- State Biot-Savart law in vector form. Derive B at centre of circular loop.
- State Ampere’s circuital law. Derive B inside a long solenoid.
- What is Lorentz force? Write its expression.
- What is cyclotron? Derive cyclotron frequency. Why can it not accelerate electrons?
- Two parallel wires carry currents I₁ and I₂. Derive force per unit length.
- Derive expression for force on moving charge in combined E and B fields.
- What is a moving coil galvanometer? Derive its current sensitivity.
- Convert MCG to ammeter and voltmeter — explain.
- State the right-hand rule for direction of magnetic field around a wire.
- What are radial and uniform fields? Why are radial fields used in galvanometers?
- Derive expression for B on axis of circular loop.
- What is a toroid? Derive expression for B inside it.
- Define magnetic moment. Calculate moment of a 50-turn loop carrying 2 A in 0.01 m² area.
- Calculate torque on a coil of N=20 turns, A=10 cm², I=0.5 A in B=0.1 T at 30° to B.
- What is the Hall effect? Mention one application.
- Calculate cyclotron frequency for a proton in B=1 T.
- What is the maximum KE of an alpha particle in cyclotron with r=0.5 m, B=1 T?
- Two long parallel straight wires 1 cm apart carry equal currents 5 A in same direction. Force per metre?
- A solenoid is 1 m long, has 1000 turns, carries 2 A. Find B at centre.
- Define Bohr magneton. Give its numerical value.
Numerical Worked Example
Q. A solenoid of length 0.5 m has 5000 turns and carries 4 A. Find B inside the solenoid.
A. n = N/L = 5000/0.5 = 10,000 turns/m. B = μ₀nI = 4π × 10⁻⁷ × 10,000 × 4 = 5.03 × 10⁻² T = 0.0503 T.
FAQ
What is the weightage of Chapter 4 Moving Charges and Magnetism in CBSE Class 12 board?
5–7 marks in CBSE board exam, typically as 1 derivation question + 1 numerical or short-answer question. JEE/NEET weightage is 3–4 questions out of Physics.
Which derivation is most asked in board exams?
B at the centre of a circular loop using Biot-Savart law, B inside a long solenoid using Ampere’s law, and force per unit length between two parallel wires.
Why does cyclotron not work for electrons?
Electrons are very light, so even at modest energies they reach relativistic speeds. Mass becomes velocity-dependent; cyclotron frequency is no longer constant, and synchronisation with the AC voltage breaks. Synchrotrons solve this.
What is the difference between current sensitivity and voltage sensitivity of MCG?
Current sensitivity = φ/I = NAB/k. Voltage sensitivity = φ/V = NAB/(kR). Increasing turns increases both, but increasing R increases current sensitivity more than voltage sensitivity.
