Magnetic Effects of Current Class 12 Formulas Sheet: Biot-Savart to Galvanometer

Moving Charges and Magnetism is about 5–6 marks in boards and 2 questions in JEE/NEET. The chapter is formula-heavy, so keep this sheet handy.

Field due to currents

• Biot–Savart: dB = (μ₀/4π) I dl sin θ / r²; μ₀ = 4π × 10⁻⁷ T m/A
• Infinite straight wire: B = μ₀I/2πr
• Centre of a circular loop: B = μ₀NI/2R; on axis: B = μ₀NIR²/2(R² + x²)^(3/2)
• Solenoid: B = μ₀nI (n = turns per metre); toroid: B = μ₀NI/2πr
• Ampère’s law: ∮B·dl = μ₀I_enclosed

Force on charges and wires

• Lorentz: F = q(v × B) = qvB sin θ; magnetic force does no work
• Circular path: r = mv/qB; T = 2πm/qB (independent of speed) — basis of the cyclotron
• Wire: F = I(l × B) = BIl sin θ
• Two parallel wires: F/l = μ₀I₁I₂/2πd; same direction attract

Torque and galvanometer

• Magnetic moment m = NIA; torque τ = mB sin θ
• Galvanometer: I = (k/NAB) θ; sensitivity ∝ NAB/k
• Ammeter: shunt S = I_gG/(I − I_g) in parallel
• Voltmeter: series resistance R = V/I_g − G

Example

A galvanometer of 100 Ω gives full deflection at 1 mA. To read 1 A: S = 0.001 × 100/(0.999) ≈ 0.1 Ω. To read 10 V: R = 10/0.001 − 100 = 9900 Ω.

Common mistakes

• Wrong direction from the right-hand rule
• Using μ₀I/2πr for a loop centre
• Confusing n (per metre) with N (total turns)

Related: Current electricity formulas.

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Frequently asked questions

Are these Magnetic Effects of Current Class 12 Formulas Sheet notes enough for the exam?

They cover every formula, definition and question type that appears in school and board papers for this chapter. Use them with the NCERT examples, exercise questions and the last five years' papers to be fully prepared.

How should I revise Magnetic Effects of Current Class 12 Formulas Sheet?

Revise the notes after 1 day, 7 days and 30 days. Solve five questions each time instead of only reading, and keep an error list of the steps you get wrong.

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