Class 12 Physics Chapter 4: Moving Charges and Magnetism
CBSE 2026–27 | NCERT-aligned free study resource
1. Magnetic Force on a Moving Charge
A charge q moving with velocity v in magnetic field B experiences F = q(v × B), with magnitude F = qvB sinθ. The force is perpendicular to both velocity and magnetic field.
q positive: force direction from right-hand rule
F is perpendicular to v and B.
2. Motion in a Magnetic Field
If v is perpendicular to B, the particle moves in a circular path with radius r = mv/(qB). Its angular frequency is ω = qB/m and time period T = 2πm/(qB), for the ideal non-relativistic case.
3. Lorentz Force
When both electric and magnetic fields act, F = q(E + v × B). This equation unifies electric and magnetic forces on a charged particle.
4. Biot–Savart Law
The magnetic field contribution of a current element is dB = (μ₀/4π) I(dℓ × r̂)/r². Direction follows the right-hand rule.
5. Magnetic Field Due to Common Current Distributions
| Source | Result |
|---|---|
| Long straight wire | B = μ₀I/(2πr) |
| Centre of circular loop | B = μ₀I/(2R) |
| Long solenoid | B ≈ μ₀nI inside |
6. Ampere’s Circuital Law
∮B·dl = μ₀Ienclosed. It is particularly useful for highly symmetric current distributions.
↺ ↺ ↺ magnetic field lines
For a straight wire, field lines form concentric circles.
7. Force on a Current-Carrying Conductor
For a straight conductor of length L carrying current I in field B, F = I(L × B). Direction follows Fleming’s left-hand rule or the vector cross product.
8. Force Between Parallel Currents
Two long parallel conductors carrying currents exert forces on each other. Currents in the same direction attract; opposite directions repel.
9. Moving Coil Galvanometer
A current-carrying coil in a magnetic field experiences torque. A galvanometer can be converted into an ammeter or voltmeter by adding suitable resistances.
Worked Example
An electron moves perpendicular to a 0.20 T magnetic field at 2×10⁶ m/s. Its circular-path radius is r = mv/(eB), giving approximately 5.7×10⁻⁵ m.
Common Exam Traps
- A stationary charge does not experience magnetic force.
- Magnetic force does no work on a point charge because it is perpendicular to instantaneous velocity.
- Use the right-hand rule carefully and account for negative charge for electrons.
Practice Questions
- Derive the radius and time period of circular motion of a charged particle in a uniform B field.
- State and explain Biot–Savart law.
- Use Ampere’s law for a long straight conductor.
- Explain the working principle of a moving-coil galvanometer.
- Why does magnetic force do no work on a charged particle?
Essential Magnetic Diagrams & Numericals
Force on a Current-Carrying Conductor
B ⊙ out of page
F = I L × B
The direction of force is perpendicular to both current direction and magnetic field. Use the right-hand rule carefully.
Charged Particle in Uniform B
When velocity is perpendicular to a uniform magnetic field, the magnetic force provides centripetal force and the particle follows circular motion: qvB=mv²/r.
Worked Numerical
For a charge q moving with speed v perpendicular to B, r=mv/(|q|B). Check SI units before substitution.
Biot–Savart and Ampere
Use the Biot–Savart law for field contributions from current elements and Ampere’s circuital law for highly symmetric current distributions.
CBSE-Style Practice
- Find magnetic force on a moving charge.
- Calculate force on a current-carrying wire.
- Find the radius of charged-particle motion.
- Use Biot–Savart law for a standard geometry.
- Apply Ampere’s law to a long straight conductor/solenoid where applicable.
Common Mistakes to Avoid
- Using the wrong direction for magnetic force.
- Forgetting that magnetic force is zero when velocity is parallel to the field.
- Mixing Biot–Savart and Ampere-law conditions of use.