Formula CheatsheetCBSE & ICSEClass 12PhysicsCh-4Verified Faculty Notes & Solutions
Magnetic Effect Of Current- Class 12 Ch-4
Formula Sheet
4 students readUpdated 1 October 2026
Formula Sheet
Class 12 Physics Formula Sheet
Moving Charges & Magnetism — Complete Revision Guide
1. Magnetic Force & Lorentz Force
- Magnetic Force on a Moving Charge: F = qvB sin(θ [theta]) (Vector form: F = q(v × B))
- Lorentz Force (Combined Electric & Magnetic): F = qE + q(v × B)
- Radius of Circular Path in Magnetic Field: r = mv / (qB) = √(2mK) / (qB)
- Time Period & Frequency: T = 2π [pi] m / (qB) and f = 1 / T = qB / (2π [pi] m)
2. Biot-Savart Law & Magnetic Field Calculations
- Biot-Savart Law: dB = (μ0 [mu_zero] / 4π) × [Idl sin(θ [theta]) / r2]
- Magnetic Field due to Straight Wire: B = (μ0I / 4πr) × (sin(φ1 [phi_1]) + sin(φ2 [phi_2])) For infinitely long wire: B = μ0I / (2πr)
- Magnetic Field at Center of Circular Coil: B = μ0IN / (2r) (N = number of turns)
- Magnetic Field on Axis of Circular Loop: B = μ0IR2N / [2(R2 + x2)3/2]
3. Ampere’s Circuital Law & Applications
- Ampere’s Circuital Law: ∫ B · dl = μ0Ienclosed
- Magnetic Field inside a Long Solenoid: B = μ0nI (where n = N / L = turns per unit length)
- Magnetic Field inside a Toroid: B = μ0NI / (2πr)
4. Force on Current-Carrying Conductors & Between Wires
- Magnetic Force on Current Wire: F = I(L × B) = ILB sin(θ [theta])
- Force Between Two Parallel Long Wires: F/l = μ0I1I2 / (2πd) (Attracts if currents are in same direction, repels if opposite)
5. Torque & Moving Coil Galvanometer
- Torque on Current Loop: τ [tau] = NIAB sin(θ [theta]) (Vector form: τ = M × B, where Magnetic Moment M = NIA)
- Moving Coil Galvanometer Equilibrium: NIAB = kφ [phi] (k = restoring torque per unit twist, φ = deflection)
- Current Sensitivity (SI) & Voltage Sensitivity (SV): SI = φ [phi] / I = NAB / k and SV = φ [phi] / V = SI / R
- Conversion of Galvanometer:
• To Ammeter: Connect a small shunt resistance (S) in parallel: S = IgG / (I - Ig)
• To Voltmeter: Connect a high resistance (R) in series: R = (V / Ig) - G
Key Formulas (Most Frequently Used)
- Magnetic Force: F = q(v × B) and F = I(L × B)
- Circular Motion Radius: r = mv / (qB)
- Long Straight Wire Field: B = μ0I / (2πr)
- Solenoid Field: B = μ0nI
- Parallel Wires Force per unit length: F/l = μ0I1I2 / (2πd)
- Torque on Loop: τ [tau] = MB sin(θ [theta])
Important Constants & Units
- Permeability of Free Space (μ0): 4π × 10-7 T·m/A
- Magnetic Field (B): 1 Tesla (T) = 1 Weber/m2 = 104 Gauss (G)
- Magnetic Flux (Φ): 1 Weber (Wb) = 1 T·m2 = 108 Maxwell
Board Important Questions & Derivations
- Derivation 1: Using Biot-Savart law, derive the expression for the magnetic field at the axis of a circular current loop.
- Derivation 2: State Ampere's circuital law and use it to find the magnetic field inside a long solenoid.
- Derivation 3: Derive the expression for the force between two infinite parallel current-carrying conductors and define 1 Ampere.
- Derivation 4: Find the torque experienced by a rectangular current loop in a uniform magnetic field.
- Conceptual Q: Why does a moving charge experience no magnetic force when moving parallel to the field?
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