Magnetic Effect of Current
Complete Formula Sheet & Shortcut Bible · BITSAT 2026
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Biot-Savart Law & Applications
Biot-Savart Law
dB = (μ₀/4π) * (I dl × r̂) / r²
|dB| = (μ₀/4π) * (Idl sinθ / r²)
|dB| = (μ₀/4π) * (Idl sinθ / r²)
Straight Wire (Finite)
B = (μ₀I/4πa) * (sinθ₁ + sinθ₂)
a is the perpendicular distance from the wire.
Straight Wire (Infinite)
B = μ₀I / 2πa
A special case of the finite wire where θ₁=θ₂=90°.
Circular Loop (Center)
B = μ₀I / 2R
Direction found using Right-Hand Thumb Rule.
Circular Loop (Axis)
B = μ₀IR² / 2(x² + R²)³/²
x is the distance from the center along the axis.
Arc at Center
B = (μ₀I/4πR) * θ
θ must be in radians.
Ampere's Law & Applications
Ampere's Circuital Law
∮ B ⋅ dl = μ₀Ienclosed
Useful for symmetric current distributions.
Solenoid (inside, long)
B = μ₀nI
n = N/L (turns per unit length). B is nearly zero outside.
Toroid (inside)
B = μ₀NI / 2πr
N = total number of turns. B is zero outside the toroid.
Thick Wire (r ≥ R)
B = μ₀I / 2πr
Outside the wire, it behaves like a thin wire.
Thick Wire (r < R)
B = (μ₀Ir) / (2πR²)
Inside the wire, B is directly proportional to r.
Lorentz Force & Force on Conductors
Lorentz Force
F = q(E + v × B)
Total force on a charge in electric and magnetic fields.
Magnetic Force on Charge
F = qvB sinθ
Direction by Fleming's Left-Hand Rule or cross product.
Force on a Wire
F = I(L × B)
F = BIL sinθ
F = BIL sinθ
Force between Parallel Wires
F/L = μ₀I₁I₂ / 2πd
Attractive for same direction currents, repulsive for opposite.
Radius of Circular Path
r = mv / qB
When a charge enters a B-field perpendicularly.
Time Period of Revolution
T = 2πm / qB
Independent of velocity (v) and radius (r).
Torque, Moment & Galvanometer
Magnetic Dipole Moment
M = NIA
Vector quantity, direction perpendicular to the loop area.
Torque on a Current Loop
τ = M × B
τ = MB sinθ = NIAB sinθ
τ = MB sinθ = NIAB sinθ
Galvanometer to Ammeter
S = IgG / (I - Ig)
Connect a low resistance shunt (S) in parallel.
Galvanometer to Voltmeter
R = (V/Ig) - G
Connect a high resistance (R) in series.
Quick Problem-Solving Hacks
Parallel Wires: Same direction currents Attract, Opposite currents Repel.
Magnetic force F = q(v × B) is always perpendicular to v. Hence, it does NO WORK and kinetic energy/speed of the particle remains constant.
Path of a charged particle in a uniform B-field:
• θ = 0° or 180° → Straight Line
• θ = 90° → Circle
• Other θ → Helix
• θ = 0° or 180° → Straight Line
• θ = 90° → Circle
• Other θ → Helix
Time period (T) and frequency (f) of a charged particle in a uniform B-field are independent of its velocity and the radius of its circular path.
For direction questions, always use vector rules. Right-Hand Thumb Rule for B-field from a wire, and Fleming's Left-Hand Rule for force (F-B-I).
Galvanometer Conversions at a Glance
| Characteristic | Ammeter | Voltmeter |
|---|---|---|
Connection | Shunt resistor in Parallel | High resistance in Series |
Resistance Value | Very Low (Shunt, S) | Very High (R) |
Ideal Resistance | Zero | Infinity |
Formula | S = IgG / (I - Ig) | R = (V / Ig) - G |