Home › Physics Class 12 · Part 1 › Moving Charges and Magnetism
Moving Charges and Magnetism
Physics · Class 12 · Part 1NCERT pp. 107–1322 sets × 25 questions
Key facts and formulas for Moving Charges and Magnetism, three worked sample questions, and two full practice sets. Every question has a hint, a reason for every option and a step-by-step solution, with a calculator or animation where one helps. English and Hinglish.
Formula sheet for this chapter
| Idea | Rule or fact |
|---|
| Force on a moving charge | F = qvB sinθ, direction by v × B (reverse for negative charge) |
| Circular motion in B | r = mv/(qB) = √(2mK)/(qB), T = 2πm/(qB), f = qB/(2πm) |
| Helix pitch | pitch = (v cosθ) × T, with v cosθ the component along B |
| Velocity selector | qE = qvB, so v = E/B |
| Biot–Savart, loop | dB = (μ₀/4π) I dl sinθ/r²; centre of loop B = μ₀I/2R |
| Loop on its axis | B = μ₀IR² / [2(x²+R²)^(3/2)] |
| Ampere's law fields | Wire: μ₀I/2πr outside, μ₀Ir/2πa² inside; solenoid μ₀nI; toroid μ₀NI/2πr |
| Parallel wires | f = μ₀I₁I₂/2πd = 2×10⁻⁷ I₁I₂/d per metre; same direction attract |
| Coil in field | τ = NIAB sinθ (θ between normal and B), m = NIA |
| Galvanometer conversions | Voltmeter: R = V/Ig − G; ammeter shunt: S = G/(n−1) |
Three sample questions
Q1. In Oersted's experiment, a compass needle placed near a long straight current-carrying wire settles
- along the wire
- along a tangent to a circle around the wire, in a plane at right angles to the wire
- pointing straight at the wire
- along the radius, away from the wire
Hint and solution
Hint: A compass needle always lines up with the local magnetic field. What shape do the field lines of a straight wire have?
- Needle aligns with local B — A compass needle turns until it lies along the magnetic field at its position.
- Straight wire: B in circles — Oersted found that the field of a long straight current forms concentric circles around the wire, in planes perpendicular to it.
- Needle along the tangent — The field direction at any point is the tangent to the circle through that point, so the needle points along that tangent.
- Answer: tangent, perpendicular plane — So the needle settles along a tangent to a circle around the wire, in a plane at right angles to the wire. Option B.
Answer: B. The needle lines up with the field, which circles the wire in a plane perpendicular to it.
Q2. An electron moves along +x in a magnetic field along +z. The force on it points along
- −y
- +x
- −z
- +y
Hint and solution
Hint: First find v × B for a positive charge using x̂ × ẑ, then remember the electron is negative.
- F = q (v × B) — The force is the charge times the cross product of velocity and field.
- x̂ × ẑ = −ŷ — Using the right hand rule, x cross z gives minus y. This is the direction for a positive charge.
- Electron: q < 0, reverse — The electron has negative charge, so the force points opposite to −y.
- Answer: +y — So the force on the electron is along +y. Option D.
Answer: D. v × B = x̂ × ẑ = −ŷ for a positive charge. For an electron the sign reverses, so +y.
Q3. A proton of kinetic energy K moves in a circle of radius r in a field B. A deuteron (charge e, mass 2m) in the same field and with the same radius has kinetic energy
- K / 2
- K
- 2K
- K / 4
Hint and solution
Hint: Write the radius in terms of kinetic energy: r = mv/qB and K = ½mv². Keep r, B and charge fixed.
- r = mv/(qB), K = ½mv² — The radius of the circle depends on momentum, and K relates to the speed.
- r = √(2mK)/(qB) — Substituting v = √(2K/m) gives this form, so K = q²B²r²/(2m).
- K ∝ q²/m at fixed B, r — Deuteron has the same charge but twice the mass, so K becomes K/2.
- Answer: K/2 — The deuteron needs half the kinetic energy. Option A.
Answer: A. r = √(2mK)/(qB), so K ∝ q²/m. Deuteron: same q, double m, so K/2.
How to use this chapter
Read the NCERT pages first, then attempt Set 1 without the hints. Note every wrong answer in a mistake list, read the reason for each option, and retry Set 2 two days later. A topic is solid when you can say why each wrong option is wrong.