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Magnetism formulas

Master Magnetism through 34 JEE Advanced-level formulas, systematically structured with every variable spelled out. Revise concept-wise, identify the areas where you need improvement, and focus your preparation with greater precision.

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Magnetism, every formula

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Biot–Savart law
$d B = \frac{μ _{0}}{4 π} \frac{I d l \times r ^}{r ^{2}}$
Q1MCQBiot–Savart
The Biot–Savart law gives the field of a current element as:
- A
  $\dfrac{\mu_0}{4\pi}\dfrac{I\,d\vec l\times\hat r}{r^{2}}$
- B
  $\dfrac{\mu_0 I}{2\pi r}$
- C
  $\dfrac{\mu_0 I}{2r}$
- D
  $\mu_0 nI$
Field of a straight wire
$B = \frac{μ _{0} I}{4 π d} (sin θ_{1} + sin θ_{2})$
Q1MCQStraight wire
The field of a finite straight wire at distance $d$ is:
- A
  $\dfrac{\mu_0 I}{4\pi d}(\sin\theta_1+\sin\theta_2)$
- B
  $\dfrac{\mu_0 I}{2\pi d}$
- C
  $\dfrac{\mu_0 I}{2d}$
- D
  $\mu_0 I d$
Field of an infinite wire
$B = \frac{μ _{0} I}{2 π r}$
Q1MCQInfinite wire
The field of an infinite straight wire is:
- A
  $\dfrac{\mu_0 I}{2\pi r}$
- B
  $\dfrac{\mu_0 I}{4\pi r}$
- C
  $\dfrac{\mu_0 I}{2r}$
- D
  $\mu_0 I r$
Field at centre of a loop
$B = \frac{μ _{0} N I}{2 r}$
Q1MCQLoop centre
The field at the centre of a circular loop is:
- A
  $\dfrac{\mu_0 NI}{2r}$
- B
  $\dfrac{\mu_0 NI}{2\pi r}$
- C
  $\dfrac{\mu_0 I}{2r^{2}}$
- D
  $\mu_0 NI$
Field on the axis of a loop
$B = \frac{μ _{0} N I R ^{2}}{2 ( R ^{2} + x ^{2} ) ^{3/2}}$
Q1MCQLoop axis
The field on the axis of a loop is:
- A
  $\dfrac{\mu_0 NIR^{2}}{2(R^{2}+x^{2})^{3/2}}$
- B
  $\dfrac{\mu_0 NI}{2r}$
- C
  $\dfrac{\mu_0 I}{2\pi x}$
- D
  $0$
Field of a circular arc
$B = \frac{μ _{0} I α}{4 π r}$
α = arc angle
Q1MCQArc field
The field at the centre of a circular arc of angle $\alpha$ is:
- A
  $\dfrac{\mu_0 I\alpha}{4\pi r}$
- B
  $\dfrac{\mu_0 I}{2r}$
- C
  $\dfrac{\mu_0 I\alpha}{2\pi r}$
- D
  $\dfrac{\mu_0 I}{4\pi r}$
Field inside an infinite solenoid
$B = μ_{0} n I$
Q1MCQSolenoid
The field inside a long solenoid is:
- A
  $\mu_0 nI$
- B
  $\dfrac{\mu_0 nI}{2}$
- C
  $\dfrac{\mu_0 I}{2\pi r}$
- D
  $\mu_0 NI$
Field of a toroid
$B = μ_{0} n I, n = \frac{N}{2 π R}$
Q1MCQToroid
The field inside a toroid is:
- A
  $\mu_0 nI$ with $n=\dfrac{N}{2\pi R}$
- B
  $\dfrac{\mu_0 NI}{2R}$
- C
  $0$
- D
  $\dfrac{\mu_0 I}{2\pi R}$
Ampere's circuital law
$\oint B \cdot d l = μ_{0} I$
Q1MCQAmpere's law
Ampere's circuital law states $\oint\vec B\cdot d\vec l$ equals:
- A
  $\mu_0 I$
- B
  $\dfrac{I}{\mu_0}$
- C
  $0$
- D
  $\mu_0 I^{2}$
Force on a moving charge
$F = q (v \times B)$
Lorentz force
$F = q (E + v \times B)$
Q1MCQLorentz force
The Lorentz force on a charge is:
- A
  $q(\vec E+\vec v\times\vec B)$
- B
  $q\vec v\times\vec B$
- C
  $q\vec E$
- D
  $qvB$
Radius of circular path
$r = \frac{m v}{q B}$
Q1MCQCircular path
The radius of a charge's circular path in a field is:
- A
  $\dfrac{mv}{qB}$
- B
  $\dfrac{qB}{mv}$
- C
  $\dfrac{mvB}{q}$
- D
  $\dfrac{v}{qB}$
Time period in a field
$T = \frac{2 π m}{q B}$
Q1MCQTime period
The period of circular motion in a field is:
- A
  $\dfrac{2\pi m}{qB}$
- B
  $\dfrac{2\pi q}{mB}$
- C
  $\dfrac{2\pi mv}{qB}$
- D
  $\dfrac{qB}{2\pi m}$
Pitch of a helix
$p = \frac{2 π m v cos θ}{q B}$
Q1MCQHelical pitch
The pitch of a helical path is:
- A
  $\dfrac{2\pi mv\cos\theta}{qB}$
- B
  $\dfrac{2\pi m}{qB}$
- C
  $\dfrac{mv\sin\theta}{qB}$
- D
  $\dfrac{2\pi mv}{qB}$
Force on a current-carrying wire
$F = I (l \times B), F = B I l sin θ$
Force between parallel wires
$\frac{F}{l} = \frac{μ _{0}}{4 π} \frac{2 I _{1} I _{2}}{r}$
Q1MCQParallel wires
The force per unit length between two parallel wires is:
- A
  $\dfrac{\mu_0}{4\pi}\dfrac{2I_1 I_2}{r}$
- B
  $\dfrac{\mu_0 I_1 I_2}{r^{2}}$
- C
  $\mu_0 I_1 I_2$
- D
  $\dfrac{\mu_0}{2\pi}\dfrac{I_1 I_2}{r^{2}}$
Magnetic moment of a loop
$M = N I A$
Q1MCQLoop moment
The magnetic moment of an $N$-turn loop is:
- A
  $NIA$
- B
  $\dfrac{IA}{N}$
- C
  $NI$
- D
  $IA^{2}$
Torque on a loop
$τ = M \times B, τ = N I A B sin θ$
Q1MCQLoop torque
The torque on a current loop in a field is:
- A
  $NIAB\sin\theta$
- B
  $NIAB\cos\theta$
- C
  $NIAB$
- D
  $\dfrac{NIAB}{\sin\theta}$
Cyclotron frequency
$f = \frac{q B}{2 π m}$
Q1MCQCyclotron frequency
The cyclotron frequency is:
- A
  $\dfrac{qB}{2\pi m}$
- B
  $\dfrac{2\pi m}{qB}$
- C
  $\dfrac{qB}{m}$
- D
  $\dfrac{m}{qB}$
Gyromagnetic ratio
$\frac{M}{L} = \frac{q}{2 m}$
Q1MCQGyromagnetic ratio
The gyromagnetic ratio $M/L$ is:
- A
  $\dfrac{q}{2m}$
- B
  $\dfrac{2m}{q}$
- C
  $\dfrac{q}{m}$
- D
  $qm$
Magnetic moment of orbiting electron
$M = \frac{e v r}{2}$
Q1MCQOrbiting electron
The magnetic moment of an electron orbiting at radius $r$, speed $v$ is:
- A
  $\dfrac{evr}{2}$
- B
  $evr$
- C
  $\dfrac{ev}{2r}$
- D
  $\dfrac{er}{2v}$
Bar magnet moment
$M = m l$
m = pole strength, l = length
Q1MCQBar magnet moment
The magnetic moment of a bar magnet is:
- A
  $m\,l$
- B
  $\dfrac{m}{l}$
- C
  $m+l$
- D
  $ml^{2}$
Field of a magnet (axial)
$B = \frac{μ _{0}}{4 π} \frac{2 M}{r ^{3}}$
Q1MCQMagnet axial
The field of a magnet on its axis is:
- A
  $\dfrac{\mu_0}{4\pi}\dfrac{2M}{r^{3}}$
- B
  $\dfrac{\mu_0}{4\pi}\dfrac{M}{r^{3}}$
- C
  $\dfrac{\mu_0}{4\pi}\dfrac{2M}{r^{2}}$
- D
  $\dfrac{\mu_0 M}{r}$
Field of a magnet (equatorial)
$B = \frac{μ _{0}}{4 π} \frac{M}{r ^{3}}$
Q1MCQMagnet equatorial
The field of a magnet on its equatorial line is:
- A
  $\dfrac{\mu_0}{4\pi}\dfrac{M}{r^{3}}$
- B
  $\dfrac{\mu_0}{4\pi}\dfrac{2M}{r^{3}}$
- C
  $\dfrac{\mu_0 M}{r^{2}}$
- D
  $0$
Torque on a magnet
$τ = M B sin θ$
Q1MCQMagnet torque
The torque on a magnet in a field is:
- A
  $MB\sin\theta$
- B
  $MB\cos\theta$
- C
  $MB$
- D
  $\dfrac{MB}{\sin\theta}$
PE of a magnet
$U = - M B cos θ$
Q1MCQMagnet PE
The potential energy of a magnet in a field is:
- A
  $-MB\cos\theta$
- B
  $MB\cos\theta$
- C
  $MB\sin\theta$
- D
  $-MB$
Work to rotate a magnet
$W = M B (cos θ_{1} - cos θ_{2})$
Q1MCQRotating a magnet
The work to rotate a magnet from $\theta_1$ to $\theta_2$ is:
- A
  $MB(\cos\theta_1-\cos\theta_2)$
- B
  $MB(\cos\theta_2-\cos\theta_1)$
- C
  $MB\sin\theta$
- D
  $0$
Earth's horizontal component
$B_{H} = B cos δ$
Q1MCQHorizontal component
The horizontal component of Earth's field is:
- A
  $B\cos\delta$
- B
  $B\sin\delta$
- C
  $B\tan\delta$
- D
  $B$
Angle of dip
$tan δ = \frac{B _{V}}{B _{H}}$
Q1MCQAngle of dip
The angle of dip satisfies:
- A
  $\tan\delta=\dfrac{B_V}{B_H}$
- B
  $\tan\delta=\dfrac{B_H}{B_V}$
- C
  $\sin\delta=\dfrac{B_V}{B}$
- D
  $\delta=B_V B_H$
Magnetic susceptibility
$χ = \frac{I}{H}$
Q1MCQSusceptibility
The magnetic susceptibility is:
- A
  $\dfrac{I}{H}$
- B
  $\dfrac{H}{I}$
- C
  $IH$
- D
  $\dfrac{B}{H}$
Relative permeability
$μ_{r} = 1 + χ$
Q1MCQRelative permeability
The relative permeability is related to susceptibility by:
- A
  $\mu_r=1+\chi$
- B
  $\mu_r=1-\chi$
- C
  $\mu_r=\chi$
- D
  $\mu_r=\dfrac{1}{\chi}$
Moving-coil galvanometer
$I = \frac{C}{N A B} θ$
Q1MCQGalvanometer
In a moving-coil galvanometer, the current is:
- A
  $\dfrac{C}{NAB}\theta$
- B
  $NAB\theta$
- C
  $\dfrac{NAB}{C}\theta$
- D
  $C\theta$
Tangent galvanometer
$B_{c} = B_{H} tan θ$
Q1MCQTangent galvanometer
In a tangent galvanometer, the coil field balances as:
- A
  $B_c=B_H\tan\theta$
- B
  $B_c=B_H\sin\theta$
- C
  $B_c=B_H\cos\theta$
- D
  $B_c=B_H$
Vibration magnetometer period
$T = 2 π \frac{I}{M B _{H}}$
Q1MCQVibration magnetometer
The period of a vibration magnetometer is:
- A
  $2\pi\sqrt{\dfrac{I}{MB_H}}$
- B
  $2\pi\sqrt{\dfrac{MB_H}{I}}$
- C
  $2\pi\sqrt{\dfrac{I}{M}}$
- D
  $2\pi\sqrt{I B_H}$

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Magnetism formulas

Magnetism, every formula

Biot–Savart law

Field of a straight wire

Field of an infinite wire

Field at centre of a loop

Field on the axis of a loop

Field of a circular arc

Field inside an infinite solenoid

Field of a toroid

Ampere's circuital law

Force on a moving charge

Lorentz force

Radius of circular path

Time period in a field

Pitch of a helix

Force on a current-carrying wire

Force between parallel wires

Magnetic moment of a loop

Torque on a loop

Cyclotron frequency

Gyromagnetic ratio

Magnetic moment of orbiting electron

Bar magnet moment

Field of a magnet (axial)

Field of a magnet (equatorial)

Torque on a magnet

PE of a magnet

Work to rotate a magnet

Earth's horizontal component

Angle of dip

Magnetic susceptibility

Relative permeability

Moving-coil galvanometer

Tangent galvanometer

Vibration magnetometer period

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