Physics · Electromagnetism

Magnetic Effects of Current and Magnetism formulas for JEE

Every Magnetic Effects of Current and Magnetism formula you need for JEE, grouped by concept.

FormulasRevision notes
37 formulas3 concepts
01Magnetic Field and Laws02Magnetic Force03Magnetic Dipoles and Materials
01

Magnetic Field and Laws

11 formulas

Ampere's Circuital Law

∮B⋅dl=μ0Ienc\oint \mathbf{B} \cdot d\mathbf{l} = \mu_0 I_{enc}

Line integral of magnetic field around a closed loop.

applies whenSteady currents.
amperelaw

Magnetic Field of Circular Arc

B=μ0I4πRθB = \frac{\mu_0 I}{4\pi R} \theta

Magnetic field at the center of a circular arc subtending angle theta.

applies whenTheta must be in radians.
arccenterjee-advanced

Biot-Savart Law

dB=μ04πIdl×rr3d\mathbf{B} = \frac{\mu_0}{4\pi} \frac{I d\mathbf{l} \times \mathbf{r}}{r^3}

Magnetic field produced by an infinitesimal current element.

applies whenSteady currents.
biot_savartfield

Field Inside Solid Cylinder

B=μ0Ir2πa2B = \frac{\mu_0 I r}{2\pi a^2}

Magnetic field inside a solid cylindrical wire with uniform current density.

applies whenDistance r < a (radius of wire), uniform current distribution.
cylinderinsideampere

Magnetic Field on Loop Axis

B=μ0IR22(x2+R2)3/2i^\mathbf{B} = \frac{\mu_0 I R^2}{2(x^2 + R^2)^{3/2}} \hat{i}

Magnetic field on the axis of a circular current loop at distance x from center.

applies whenOn the central axis of the circular loop.
loopaxis

Magnetic Field at Loop Center

B=μ0I2RB = \frac{\mu_0 I}{2R}

Magnetic field at the center of a circular current loop.

applies whenAt the geometric center of the loop.
loopcenter

Magnetic Field of Ideal Solenoid

B=μ0nIB = \mu_0 n I

Magnetic field deep inside a long ideal solenoid.

applies whenLong solenoid, well inside the ends.
solenoidinterior

Magnetic Field at Solenoid End

B=μ0nI2B = \frac{\mu_0 n I}{2}

Magnetic field exactly at the open end of a semi-infinite solenoid.

applies whenAt the edge of a long solenoid.
solenoidendjee-advanced

Magnetic Field Inside Toroid

B=μ0NI2πrB = \frac{\mu_0 N I}{2\pi r}

Magnetic field confined within the core of a toroid.

applies whenInside the toroid core.
toroidinteriorjee-advanced

Magnetic Field of Long Wire

B=μ0I2πrB = \frac{\mu_0 I}{2\pi r}

Magnetic field at a distance r from an infinitely long straight wire.

applies whenInfinite straight wire.
infinite_wirefield

Magnetic Field of Finite Wire

B=μ0I4πd(sin⁡θ1+sin⁡θ2)B = \frac{\mu_0 I}{4\pi d} (\sin\theta_1 + \sin\theta_2)

Magnetic field at a perpendicular distance d from a finite straight wire.

applies whenFinite straight wire, angles measured from perpendicular.
finite_wirejee-advanced
02

Magnetic Force

9 formulas

Cyclotron Angular Frequency

ω=qBm\omega = \frac{qB}{m}

Angular frequency of a charged particle in a uniform magnetic field.

applies whenNon-relativistic speeds.
cyclotronfrequency

Magnetic Force Magnitude

F=qvBsin⁡θF = qvB\sin\theta

Magnitude of the magnetic force on a moving charge.

applies whenAngle \theta is between velocity and magnetic field vectors.
magneticforce

Force Between Parallel Currents

f=μ0IaIb2πdf = \frac{\mu_0 I_a I_b}{2\pi d}

Magnetic force per unit length between two infinite parallel current-carrying wires.

applies whenInfinite, parallel straight wires.
forceparallel_wires

Magnetic Force on Straight Wire

F=I(l×B)\mathbf{F} = I(\mathbf{l} \times \mathbf{B})

Force on a straight current-carrying conductor in a uniform magnetic field.

applies whenUniform magnetic field and straight wire.
forceconductor

Magnetic Force on Arbitrary Wire

F=∫I(dl×B)\mathbf{F} = \int I (d\mathbf{l} \times \mathbf{B})

Force on an arbitrarily shaped current-carrying wire.

applies whenIntegration over the length of the conductor.
forceconductorintegration

Pitch of Helical Path

p=v∥T=2πmvcos⁡θqBp = v_{\parallel} T = \frac{2\pi m v \cos\theta}{qB}

Linear distance traveled along the magnetic field per revolution.

applies whenVelocity has a component parallel to the uniform magnetic field.
helical_motionpitch

Lorentz Force

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

Total force on a charge moving in electric and magnetic fields.

applies whenApplicable for point charges.
lorentzforce

Radius of Circular Path

r=mvqB=pqB=2mKqBr = \frac{mv}{qB} = \frac{p}{qB} = \frac{\sqrt{2mK}}{qB}

Radius of the circular trajectory of a charged particle in a perpendicular magnetic field.

applies whenVelocity must be perpendicular to uniform magnetic field.
circular_motioncyclotronjee-advanced

Torque on Current Loop (Scalar)

τ=NIABsin⁡θ\tau = N I A B \sin\theta

Magnitude of torque on a current loop in a magnetic field.

applies whenUniform magnetic field.
torqueloop
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03

Magnetic Dipoles and Materials

17 formulas

Ammeter Shunt Resistance

rs=IgRGI−Igr_s = \frac{I_g R_G}{I - I_g}

Shunt resistance required to convert a galvanometer into an ammeter.

applies whenDesired range I, galvanometer full scale current I_g.
ammeterconversionjee-advanced

Axial Field of Dipole

BA=μ04π2mr3\mathbf{B}_A = \frac{\mu_0}{4\pi} \frac{2\mathbf{m}}{r^3}

Magnetic field on the axial line of a short magnetic dipole.

applies whenShort dipole approximation (r >> l).
dipoleaxis

Equatorial Field of Dipole

BE=−μ04πmr3\mathbf{B}_E = -\frac{\mu_0}{4\pi} \frac{\mathbf{m}}{r^3}

Magnetic field on the equatorial line of a short magnetic dipole.

applies whenShort dipole approximation (r >> l).
dipoleequator

Potential Energy of Dipole

U=−m⋅BU = -\mathbf{m} \cdot \mathbf{B}

Potential energy of a magnetic dipole in a uniform magnetic field.

applies whenUniform magnetic field.
energydipole

Gauss's Law for Magnetism

∮B⋅dS=0\oint \mathbf{B} \cdot d\mathbf{S} = 0

The net magnetic flux through any closed surface is identically zero.

applies whenValid for any closed surface.
gauss_lawflux

Current Sensitivity

Is=ϕI=NABkI_s = \frac{\phi}{I} = \frac{NAB}{k}

Deflection per unit current in a Moving Coil Galvanometer.

galvanometersensitivity

Magnetic Intensity

H=Bμ0−M\mathbf{H} = \frac{\mathbf{B}}{\mu_0} - \mathbf{M}

Magnetic intensity or magnetising field vector.

intensitymaterials

Magnetisation

M=mnetV\mathbf{M} = \frac{\mathbf{m}_{net}}{V}

Net magnetic moment per unit volume.

applies whenBulk materials.
magnetisationmaterials

Magnetic Field in Material

B=μ0(H+M)\mathbf{B} = \mu_0(\mathbf{H} + \mathbf{M})

Total magnetic field inside a magnetic material.

fieldmaterials

Galvanometer Equilibrium

kϕ=NIABk\phi = N I A B

Torque balance equation for a Moving Coil Galvanometer.

applies whenRadial magnetic field.
galvanometerequilibrium

Magnetic Dipole Moment of Loop

m=NIA\mathbf{m} = N I \mathbf{A}

Magnetic moment vector of a current carrying loop.

applies whenPlanar loop of area A and N turns.
dipolemoment

Relative Permeability

μr=1+χ\mu_r = 1 + \chi

Relationship between relative permeability and magnetic susceptibility.

applies whenLinear magnetic materials.
permeabilitymaterials

Magnetic Susceptibility

M=χH\mathbf{M} = \chi \mathbf{H}

Relation between Magnetisation and Magnetic Intensity in linear materials.

applies whenLinear isotropic magnetic materials.
susceptibilitymaterials

Torque on Magnetic Dipole

τ=m×B\boldsymbol{\tau} = \mathbf{m} \times \mathbf{B}

Vector torque experienced by a magnetic dipole in a uniform magnetic field.

applies whenUniform magnetic field.
torquedipole

Torque on Current Loop (Scalar)

τ=NIABsin⁡θ\tau = N I A B \sin\theta

Magnitude of torque on a current loop in a magnetic field.

applies whenUniform magnetic field.
torqueloop

Voltmeter Series Resistance

R=VIg−RGR = \frac{V}{I_g} - R_G

Series resistance required to convert a galvanometer into a voltmeter.

applies whenDesired range V, galvanometer full scale current I_g.
voltmeterconversionjee-advanced

Voltage Sensitivity

Vs=ϕV=NABkRGV_s = \frac{\phi}{V} = \frac{NAB}{k R_G}

Deflection per unit voltage in a Moving Coil Galvanometer.

galvanometersensitivity
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