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Cheat sheet · JEE Preparation Physics

Moving Charges and Magnetism cheat sheet

The whole chapter on one page: key formulas, facts and the points to remember, for quick revision before a test.

JEE · Physics

Cheat sheet

Class 12 · Chapter 4Moving Charges and Magnetism

Lorentz force: F = q(E + v × B).

1. Force on Charges

F⃗=qv⃗×B⃗\vec F = q\vec v\times\vec Br=mvqBr = \dfrac{mv}{qB}
F⃗=Il⃗×B⃗\vec F = I\vec l\times\vec B

Cyclotron frequency ν=qB2πm\nu = \dfrac{qB}{2\pi m} (independent of speed).

2. Magnetic Fields

SourceB
Biot–Savart elementdB=μ04πI dlsin⁡θr2dB = \dfrac{\mu_0}{4\pi}\dfrac{I\,dl\sin\theta}{r^2}
Long straight wireμ0I2πr\dfrac{\mu_0I}{2\pi r}
Centre of circular loopμ0NI2R\dfrac{\mu_0NI}{2R}
Solenoid (inside)μ0nI\mu_0nI
Toroidμ0NI2πr\dfrac{\mu_0NI}{2\pi r}

Ampère's law: ∮B⃗⋅dl⃗=μ0I\oint\vec B\cdot d\vec l = \mu_0I.

3. Forces & Torque

Fl=μ0I1I22πd\dfrac{F}{l} = \dfrac{\mu_0I_1I_2}{2\pi d}
τ=NIABsin⁡θ\tau = NIAB\sin\theta

Parallel currents attract; antiparallel repel.

4. Galvanometer

  • To ammeter: small shunt in parallel.
  • To voltmeter: large resistance in series.
S=IgGI−IgS = \dfrac{I_gG}{I - I_g}R=VIg−GR = \dfrac{V}{I_g} - G

5. Key Points

  • Magnetic force does no work.
  • μ₀ = 4π × 10⁻⁷ T m/A.
  • Radial field in moving-coil galvanometer.
  • Current loop acts as a magnetic dipole (m = NIA).

Remember: Lorentz force | B formulas | ammeter & voltmeter conversion

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