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.

36 formulas3 concepts

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QuestionState the formula — Ampere's Circuital Law

Reveal answer

Ampere's Circuital Law

\oint \mathbf{B} \cdot d\mathbf{l} = \mu_0 I_{enc}

Line integral of magnetic field around a closed loop.applies whenSteady currents.amperelaw

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All 36 Magnetic Effects of Current and Magnetism formulas

Magnetic Field and Laws

11 formulas

Ampere's Circuital Law

\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 = \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

d\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 = \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

\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 = \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 = \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 = \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 = \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 = \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 = \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

Magnetic Force

9 formulas

Cyclotron Angular Frequency

\omega = \frac{qB}{m}

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

applies whenNon-relativistic speeds.

cyclotronfrequency

Magnetic Force Magnitude

F = 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 = \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

\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

\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_{\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

\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 = \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)

\tau = N I A B \sin\theta

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

applies whenUniform magnetic field.

torqueloop

Magnetic Dipoles and Materials

16 formulas

Ammeter Shunt Resistance

r_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

\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

\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 = -\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

\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

I_s = \frac{\phi}{I} = \frac{NAB}{k}

Deflection per unit current in a Moving Coil Galvanometer.

galvanometersensitivity

Magnetic Intensity

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

Magnetic intensity or magnetising field vector.

intensitymaterials

Magnetisation

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

Net magnetic moment per unit volume.

applies whenBulk materials.

magnetisationmaterials

Magnetic Field in Material

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

Total magnetic field inside a magnetic material.

fieldmaterials

Galvanometer Equilibrium

k\phi = N I A B

Torque balance equation for a Moving Coil Galvanometer.

applies whenRadial magnetic field.

galvanometerequilibrium

Magnetic Dipole Moment of Loop

\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

\mu_r = 1 + \chi

Relationship between relative permeability and magnetic susceptibility.

applies whenLinear magnetic materials.

permeabilitymaterials

Magnetic Susceptibility

\mathbf{M} = \chi \mathbf{H}

Relation between Magnetisation and Magnetic Intensity in linear materials.

applies whenLinear isotropic magnetic materials.

susceptibilitymaterials

Torque on Magnetic Dipole

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

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

applies whenUniform magnetic field.

torquedipole

Voltmeter Series Resistance

R = \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

V_s = \frac{\phi}{V} = \frac{NAB}{k R_G}

Deflection per unit voltage in a Moving Coil Galvanometer.

galvanometersensitivity

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