“Ammeter parallel and low, voltmeter series and high”
Converting a galvanometer
An ammeter takes a small shunt in parallel; a voltmeter takes a large resistance in series. An ideal ammeter has zero resistance, an ideal voltmeter infinite.
Class 12 Physics · Gujarat Board, CBSE, GUJCET, JEE and NEET
Moving Charges and Magnetism formulas
This chapter is where the right hand earns its marks. Every formula here has a direction attached, and the numerical part is usually easier than getting that direction right, so the hand rules deserve more practice than the algebra.
17 formulas, 4 memory hooks, and the 5 mistakes that cost the most marks.
Force on charges and wires
| What | Formula | Symbols and notes |
|---|---|---|
| Lorentz force | F = qvB sinθ | maximum when the velocity is perpendicular to B, zero when parallel |
| Force on a conductor | F = BIL sinθ | the working principle of the electric motor |
| Radius in a magnetic field | r = mv/qB | the faster or heavier the particle, the wider the circle |
| Time period in a magnetic field | T = 2πm/qB | independent of speed, which is what makes the cyclotron work |
| Cyclotron frequency | f = qB/2πm | the resonance condition |
| Velocity selector | v = E/B | only this speed passes undeflected |
Fields from currents
| What | Formula | Symbols and notes |
|---|---|---|
| Biot-Savart law | dB = (μ₀/4π)(I dl sinθ)/r² | μ₀ = 4π × 10−7 T m A−1 |
| Straight infinite wire | B = μ₀I/2πr | circles around the wire, given by the right-hand grip rule |
| Centre of a circular loop | B = μ₀I/2R | perpendicular to the plane of the loop |
| On the axis of a loop | B = μ₀IR²/2(R² + x²)3/2 | reduces to μ₀I/2R at the centre |
| Long solenoid | B = μ₀nI | n is turns per unit length; the field inside is uniform |
| Toroid | B = μ₀NI/2πr | the field outside is zero |
Current loops and instruments
| What | Formula | Symbols and notes |
|---|---|---|
| Force between parallel wires | F/L = μ₀I₁I₂/2πd | same direction attracts, opposite repels |
| Magnetic moment of a loop | m = NIA | N turns, area A |
| Torque on a loop | τ = NIAB sinθ = mB sinθ | how a moving-coil galvanometer works |
| Galvanometer to ammeter | shunt S = IgG/(I − Ig) | a small resistance in parallel |
| Galvanometer to voltmeter | R = V/Ig − G | a large resistance in series |
Taught by Darshit Bhatt, founder and lead faculty at Darshit Sir Institute. Instrumentation and Control engineer, with a master's degree and a chartered degree, teaching in Paldi, Ahmedabad since 2006.
Know the formula but not when to use it?
Darshit Sir has taught this in Paldi since 2006, in the classroom and live online.
Memory hooks
How to remember this chapter.
“Same way, they hug”
Force between parallel wires
Parallel currents in the same direction attract; opposite directions repel. This is the opposite of what charges do, and it is how the ampere is defined.
“Magnetic force never does work”
Why speed does not change
The force is always perpendicular to the velocity, so it changes direction but never speed. That is why the time period does not depend on how fast the particle is going.
“Grip the wire”
Direction of the field around a wire
Thumb along the current, curled fingers give the circular field. For a loop or solenoid, curl the fingers along the current and the thumb points to the north face.
Where marks go
The mistakes that cost the most.
- Expecting a magnetic force on a charge at rest. The force needs motion, and motion not parallel to the field.
- Thinking a magnetic field speeds a particle up. It cannot; it only bends the path.
- Using B = μ₀nI with n as the total number of turns. It is turns per unit length.
- Reversing the attraction rule for parallel wires. Same direction attracts, unlike charges at rest.
- Forgetting that the field is zero outside a toroid and outside an ideal solenoid.
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