ElectromagnetismHigh Yield (2-3 Qs in JEE)

Magnetic Effects of Current Formulas

Biot-Savart law, Ampere's circuital law, magnetic field of straight wire, circular loop, solenoid, and Lorentz magnetic force.

8 Formulas•480+ Questions in Bank

Core Formulas & Mathematical Identities

\vec{F}_m = q(\vec{v} \times \vec{B}), \quad r = \frac{m v_\perp}{qB}, \quad T = \frac{2\pi m}{qB}

Force on moving charge in magnetic field and helical circular radius.

Examiner Tip: Time period and cyclotron frequency are completely independent of particle speed v.

d\vec{B} = \frac{\mu_0}{4\pi} \frac{I (d\vec{l} \times \hat{r})}{r^2}, \quad \frac{\mu_0}{4\pi} = 10^{-7} \text{ T m/A}

Fundamental differential magnetic field generated by current element.

Examiner Tip: Direction is given by right-hand palm rule.

B_{\text{wire}} = \frac{\mu_0 I}{2\pi d}, \quad B_{\text{ring, center}} = \frac{\mu_0 I}{2R}, \quad B_{\text{ring, axis}} = \frac{\mu_0 I R^2}{2(R^2 + x^2)^{3/2}}

Field formulas derived from Biot-Savart integration.

Examiner Tip: For ideal long solenoid, B = μ₀ n I inside, and 0 outside.

\frac{F}{L} = \frac{\mu_0 I_1 I_2}{2\pi d}

Attractive if currents flow in same direction; repulsive if in opposite directions.

Examiner Tip: Used to define the international Ampere standard.

\vec{M} = N I \vec{A}, \quad \vec{\tau} = \vec{M} \times \vec{B}, \quad U = -\vec{M} \cdot \vec{B}

Magnetic dipole behavior of planar current loop.

Examiner Tip: Gyromagnetic ratio for revolving electron: M / L = e / (2m).

\oint \vec{B} \cdot d\vec{l} = \mu_0 I_{\text{enc}}, \quad B_{\text{solenoid}} = \mu_0 n I, \quad B_{\text{thick wire}}(r \le R) = \frac{\mu_0 I r}{2\pi R^2}

Circuital law line integral and internal fields for infinite solenoid, toroid, and solid cylindrical conductors.

Examiner Tip: Field at the exact ends of a semi-infinite solenoid is exactly half the interior field: B_end = (1/2)μ₀ n I.

\theta = \left(\frac{NAB}{C}\right)I, \quad \text{Shunt: } S = \frac{I_g R_g}{I - I_g}, \quad \text{Multiplier: } R = \frac{V}{I_g} - R_g

Torsional suspension equilibrium and conversion into ammeter (low parallel shunt S) and voltmeter (high series resistance R).

Examiner Tip: Ideal ammeter has zero resistance; ideal voltmeter has infinite resistance.

\mu_l = \left(\frac{e}{2m}\right)L = n\mu_B, \quad \mu_B = \frac{e\hbar}{2m} = \frac{eh}{4\pi m} \approx 9.27 \times 10^{-24}\,\text{A}\cdot\text{m}^2

Magnetic moment of an electron orbiting a nucleus in the n-th Bohr orbit.

Examiner Tip: Gyromagnetic ratio e/(2m) is a universal constant independent of orbit radius and velocity.

Frequently tested misconceptions in Magnetic Effects of Current

•Magnetic force does NO WORK on a moving charged particle: W = ∫ F · v dt = 0 (velocity magnitude is constant, only direction changes).
•Radius of helical path depends on perpendicular velocity component: r = m v_⊥ / (qB).