Magnetic Effects of Current and Magnetism formulas for JEE Main & Advanced

23 formula entries for Magnetic Effects of Current and Magnetism, in the order the chapter builds them. Each shows the formula, when to use it and the first trap to avoid.

Biot-Savart Law

d \vec{B} = \frac{μ_{0}}{4 π} \frac{I d \vec{l} \times \hat{r}}{r^{2}}

When to use. To compute magnetic field due to any current-carrying conductor by integrating over the path.

Trap. Forgetting the cross product: $d \vec{B}$ is perpendicular to both $d \vec{l}$ and $\hat{r}$ .

Magnetic Field Due to a Straight Current-Carrying Wire

B = \frac{μ_{0} I}{2 π R}

When to use. For infinite or long straight wires, or segments with known angles.

Trap. Using $μ_{0} I / (2 π R)$ for a finite wire without angle correction.

Magnetic Field on Axis of a Circular Loop

B = \frac{μ_{0} I R^{2}}{2 (R^{2} + x^{2})^{3 / 2}}

When to use. For any point on the axis of a circular current loop.

Trap. At center ( $x = 0$ ), using $B = μ_{0} I / (2 R)$ correctly.

Ampere's Circuital Law

\oint \vec{B} \cdot d \vec{l} = μ_{0} I_{enc}

When to use. To find $B$ for symmetric current distributions (infinite wire, solenoid, toroid).

Trap. Only the current passing through the loop counts, not outside.

Magnetic Field Inside a Solenoid

B = μ_{0} n I

where

n = N / L

is turns per unit length.

When to use. For long, tightly wound solenoids.

Trap. Assuming field is uniform near the ends.

Magnetic Field Inside a Toroid

B = \frac{μ_{0} N I}{2 π r}

When to use. For toroidal coils with $N$ turns.

Trap. Using a fixed radius: $B = \frac{μ_{0} N I}{2 π r}$ varies with $r$ (distance of the point from the axis), from inner to outer radius; mean radius is only an approximation for a thin toroid.

Lorentz Force

\vec{F} = q (\vec{E} + \vec{v} \times \vec{B})

When to use. For any charged particle moving in electromagnetic fields.

Trap. Magnetic force does no work (perpendicular to velocity).

Motion in Uniform Magnetic Field

r = \frac{m v}{q B}

T = \frac{2 π m}{q B}

, pitch

= v_{∥} T

When to use. For charged particles in uniform $B$ .

Trap. Using $r = m v / (q B)$ for relativistic speeds (not needed in JEE).

Force on a Current-Carrying Conductor

\vec{F} = I \vec{l} \times \vec{B}

(for straight wire)

When to use. To find force on a wire segment in a magnetic field.

Trap. Direction given by Fleming's left-hand rule.

Force Between Two Parallel Currents

F / L = \frac{μ_{0} I_{1} I_{2}}{2 π d}

When to use. For long parallel wires.

Trap. Direction: same direction attract, opposite repel.

Torque on a Current Loop

\vec{τ} = \vec{m} \times \vec{B}

, where

\vec{m} = I A \hat{n}

When to use. For any current loop or coil in a magnetic field.

Trap. Torque is zero when $\vec{m}$ is parallel or anti-parallel to $\vec{B}$ .

Magnetic Moment

\vec{m} = I A \hat{n}

(for a loop)

When to use. To compute torque, potential energy, or field of a magnetic dipole.

Trap. For a solenoid, $m = N I A$ .

Moving Coil Galvanometer

θ = \frac{N I A B}{k}

(where

k

is torsional constant)

When to use. For measuring small currents.

Trap. Radial field ensures torque is proportional to current (linear scale).

Conversion of Galvanometer to Ammeter

S = \frac{I_{g} G}{I - I_{g}}

When to use. To measure large currents.

Trap. Shunt is in parallel, not series.

Conversion of Galvanometer to Voltmeter

R = \frac{V}{I_{g}} - G

When to use. To measure voltage.

Trap. Series resistance, not parallel.

Magnetic Materials: Permeability and Susceptibility

B = μ H = μ_{0} (1 + χ) H

μ_{r} = 1 + χ

When to use. To classify materials and compute fields in media.

Trap. For diamagnetic, $χ < 0$ ; paramagnetic $χ > 0$ ; ferromagnetic $χ ≫ 1$ .

Hysteresis Loop

No single formula; key parameters: retentivity, coercivity, saturation.

When to use. To understand magnetic memory and transformer cores.

Trap. Retentivity: residual $B$ when $H = 0$ .

Earth's Magnetism

Declination

δ

, dip angle

θ

, horizontal component

B_{H} = B \cos θ

When to use. For navigation and understanding magnetic field components.

Trap. Magnetic north is actually south pole (attracts north of compass).

Right-Hand Thumb Rule

No formula.

When to use. To find direction of magnetic field due to currents.

Trap. For a loop, fingers curl in current direction, thumb gives $\vec{m}$ direction.

Fleming's Left-Hand Rule

No formula.

When to use. To find direction of force on a current-carrying wire.

Trap. Only for force on a conductor, not for induced current (use right-hand rule).

Magnetic Dipole Moment of a Revolving Electron

\vec{m} = - \frac{e}{2 m} \vec{L}

When to use. In atomic physics and magnetism.

Trap. Negative sign indicates opposite direction to $\vec{L}$ .

Cyclotron

f = \frac{q B}{2 π m}

(cyclotron frequency)

When to use. To accelerate ions for nuclear physics.

Trap. Frequency independent of speed (non-relativistic).

Hall Effect

V_{H} = \frac{I B}{n e d}

(where

d

is thickness)

When to use. To determine carrier type, concentration, or magnetic field strength.

Trap. Sign of Hall voltage indicates charge carrier type (positive or negative).

Values to remember

$μ_{0} = 4 π \times 10^{- 7} T m/A$ Biot-Savart Law
$B_{earth} \approx 0.3 \times 10^{- 4} T$ to $0.6 \times 10^{- 4} T$ Earth's Magnetism
$μ_{B} = 9.27 \times 10^{- 24} J/T$ Magnetic Dipole Moment of a Revolving Electron

Read the full chapter: Magnetic Effects of Current and Magnetism for JEE, with what JEE asks and the common traps.