How much of JEE Main comes from Magnetic Effects of Current and Magnetism?

JEEGenie estimates about 5% of JEE Main marks come from Magnetic Effects of Current and Magnetism, based on recent papers. The share varies from year to year.

Which formulas matter most in Magnetic Effects of Current and Magnetism?

The Magnetic Effects of Current and Magnetism sheet on this page has 23 formula entries, starting with Biot-Savart Law, Magnetic Field Due to a Straight Current-Carrying Wire, Magnetic Field on Axis of a Circular Loop, Ampere's Circuital Law, Magnetic Field Inside a Solenoid. Each one comes with when to use it and the trap to avoid.

What topics does Magnetic Effects of Current and Magnetism cover for JEE?

Magnetic Effects of Current and Magnetism covers Biot-Savart Law, Ampere's Law, Force on a Current, Moving Charge in a Magnetic Field, Magnetic Dipole, Magnetism and Matter.

How should I revise Magnetic Effects of Current and Magnetism before the exam?

Learn each formula together with its condition of use, read the trap listed beside it, then practise questions and review every mistake. The practice link on this page opens Magnetic Effects of Current and Magnetism questions on JEEGenie.

How many previous-year questions are there on Magnetic Effects of Current and Magnetism?

JEEGenie has 411 previous-year questions on Magnetic Effects of Current and Magnetism, and this page shows a few with worked explanations.

Is practice on Magnetic Effects of Current and Magnetism free on JEEGenie?

Sign-up is free and includes a 7-day Pro trial. After the trial, free accounts keep a limited daily quota.

Magnetic Effects of Current and Magnetism for JEE Main & Advanced — formulas, what is asked, and traps

JEEGenie estimates about 5% of JEE Main marks come from Magnetic Effects of Current and Magnetism. This page covers 23 formula entries, each with when to use it, what JEE asks and the traps. A common slip: Forgetting the cross product: $d \vec{B}$ is perpendicular to both $d \vec{l}$ and $\hat{r}$ .

Key points to know

Biot-Savart Law. Gives the magnetic field $d \vec{B}$ due to a small current element $I d \vec{l}$ at a point. It is the magnetic analogue of Coulomb's law.
Ampere's Circuital Law. Line integral of magnetic field around a closed loop equals $μ_{0}$ times the net current enclosed.
Lorentz Force. Total force on a charged particle in electric and magnetic fields.
Force on a Current-Carrying Conductor. A current-carrying wire in a magnetic field experiences a force.
Torque on a Current Loop. A current loop in a uniform magnetic field experiences a torque that tends to align its magnetic moment with the field.
Magnetic Moment. Vector quantity representing the strength and orientation of a current loop's magnetic effect.
Moving Coil Galvanometer. Converts current into angular deflection using torque on a coil in a radial magnetic field.
Magnetic Materials: Permeability and Susceptibility. Permeability $μ$ relates $B$ and $H$ ; susceptibility $χ$ measures magnetization response.
Hysteresis Loop. For ferromagnetic materials, $B$ lags behind $H$ , forming a loop; area gives energy loss per cycle.
Earth's Magnetism. Earth behaves like a giant magnetic dipole with poles near geographic poles.
Magnetic Dipole Moment of a Revolving Electron. An electron orbiting a nucleus has both angular momentum and magnetic moment.
Cyclotron. Device to accelerate charged particles using perpendicular magnetic and electric fields.
Hall Effect. When a current-carrying conductor is placed in a perpendicular magnetic field, a transverse voltage (Hall voltage) develops.

Formula sheet

Name	Formula	When to use
Biot-Savart Law	$d \vec{B} = \frac{μ_{0}}{4 π} \frac{I d \vec{l} \times \hat{r}}{r^{2}}$	To compute magnetic field due to any current-carrying conductor by integrating over the path.
Magnetic Field Due to a Straight Current-Carrying Wire	$B = \frac{μ_{0} I}{2 π R}$	For infinite or long straight wires, or segments with known angles.
Magnetic Field on Axis of a Circular Loop	$B = \frac{μ_{0} I R^{2}}{2 (R^{2} + x^{2})^{3 / 2}}$	For any point on the axis of a circular current loop.
Ampere's Circuital Law	$\oint \vec{B} \cdot d \vec{l} = μ_{0} I_{enc}$	To find $B$ for symmetric current distributions (infinite wire, solenoid, toroid).
Magnetic Field Inside a Solenoid	$B = μ_{0} n I$ where $n = N / L$ is turns per unit length.	For long, tightly wound solenoids.
Magnetic Field Inside a Toroid	$B = \frac{μ_{0} N I}{2 π r}$	For toroidal coils with $N$ turns.
Lorentz Force	$\vec{F} = q (\vec{E} + \vec{v} \times \vec{B})$	For any charged particle moving in electromagnetic fields.
Motion in Uniform Magnetic Field	$r = \frac{m v}{q B}$ , $T = \frac{2 π m}{q B}$ , pitch $= v_{∥} T$	For charged particles in uniform $B$ .
Force on a Current-Carrying Conductor	$\vec{F} = I \vec{l} \times \vec{B}$ (for straight wire)	To find force on a wire segment in a magnetic field.
Force Between Two Parallel Currents	$F / L = \frac{μ_{0} I_{1} I_{2}}{2 π d}$	For long parallel wires.
Torque on a Current Loop	$\vec{τ} = \vec{m} \times \vec{B}$ , where $\vec{m} = I A \hat{n}$	For any current loop or coil in a magnetic field.
Magnetic Moment	$\vec{m} = I A \hat{n}$ (for a loop)	To compute torque, potential energy, or field of a magnetic dipole.
Moving Coil Galvanometer	$θ = \frac{N I A B}{k}$ (where $k$ is torsional constant)	For measuring small currents.
Conversion of Galvanometer to Ammeter	$S = \frac{I_{g} G}{I - I_{g}}$	To measure large currents.
Conversion of Galvanometer to Voltmeter	$R = \frac{V}{I_{g}} - G$	To measure voltage.
Magnetic Materials: Permeability and Susceptibility	$B = μ H = μ_{0} (1 + χ) H$ , $μ_{r} = 1 + χ$	To classify materials and compute fields in media.
Hysteresis Loop	No single formula; key parameters: retentivity, coercivity, saturation.	To understand magnetic memory and transformer cores.
Earth's Magnetism	Declination $δ$ , dip angle $θ$ , horizontal component $B_{H} = B \cos θ$	For navigation and understanding magnetic field components.
Right-Hand Thumb Rule	No formula.	To find direction of magnetic field due to currents.
Fleming's Left-Hand Rule	No formula.	To find direction of force on a current-carrying wire.
Magnetic Dipole Moment of a Revolving Electron	$\vec{m} = - \frac{e}{2 m} \vec{L}$	In atomic physics and magnetism.
Cyclotron	$f = \frac{q B}{2 π m}$ (cyclotron frequency)	To accelerate ions for nuclear physics.
Hall Effect	$V_{H} = \frac{I B}{n e d}$ (where $d$ is thickness)	To determine carrier type, concentration, or magnetic field strength.

Open the Magnetic Effects of Current and Magnetism formula page

What JEE asks

Biot-Savart Law. JEE often asks to derive field at center of a circular loop or on axis of a straight wire using Biot-Savart.
Magnetic Field Due to a Straight Current-Carrying Wire. JEE problems involve superposition of fields from multiple wires or finding force between parallel wires.
Magnetic Field on Axis of a Circular Loop. JEE often asks for field at center or at a distance, or for multiple coaxial loops.
Ampere's Circuital Law. JEE uses Ampere's law to derive fields for solenoids and toroids, and for coaxial cables.
Magnetic Field Inside a Solenoid. JEE problems often involve combining solenoid field with motion of charged particles.
Magnetic Field Inside a Toroid. JEE may ask for field at a point inside or compare with solenoid.
Lorentz Force. JEE often uses this for cyclotron motion, velocity selector, and Hall effect.
Motion in Uniform Magnetic Field. JEE problems: find radius, time period, or pitch; often combined with electric fields.
Force on a Current-Carrying Conductor. JEE often asks for force between parallel wires or torque on a loop.
Force Between Two Parallel Currents. JEE problems: find force per unit length, or equilibrium with other forces.
Torque on a Current Loop. JEE often asks for torque on a rectangular loop, or potential energy $U = - \vec{m} \cdot \vec{B}$ .
Magnetic Moment. JEE uses it in context of galvanometer, moving coil, and atomic magnetism.
Moving Coil Galvanometer. JEE asks for conversion to ammeter/voltmeter, or sensitivity calculations.
Conversion of Galvanometer to Ammeter. JEE problems: find shunt value for given range.
Conversion of Galvanometer to Voltmeter. JEE problems: find series resistance for given range.
Magnetic Materials: Permeability and Susceptibility. JEE asks for comparison of properties and Curie temperature.
Hysteresis Loop. JEE may ask to interpret hysteresis curves or choose material for a device.
Earth's Magnetism. JEE may ask to compute components given dip angle.
Right-Hand Thumb Rule. JEE uses it in almost every problem involving field direction.
Fleming's Left-Hand Rule. JEE often tests direction in multiple-choice questions.
Magnetic Dipole Moment of a Revolving Electron. JEE may ask for ratio of magnetic moment to angular momentum.
Cyclotron. JEE may ask for frequency or maximum kinetic energy.
Hall Effect. JEE problems: find $V_{H}$ or $n$ given parameters.

Common traps

Forgetting the cross product: $d \vec{B}$ is perpendicular to both $d \vec{l}$ and $\hat{r}$ . Biot-Savart Law
Using $μ_{0} I / (2 π R)$ for a finite wire without angle correction. Magnetic Field Due to a Straight Current-Carrying Wire
At center ( $x = 0$ ), using $B = μ_{0} I / (2 R)$ correctly. Magnetic Field on Axis of a Circular Loop
Only the current passing through the loop counts, not outside. Ampere's Circuital Law
Assuming field is uniform near the ends. Magnetic Field Inside a Solenoid
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. Magnetic Field Inside a Toroid
Magnetic force does no work (perpendicular to velocity). Lorentz Force
Using $r = m v / (q B)$ for relativistic speeds (not needed in JEE). Motion in Uniform Magnetic Field
Direction given by Fleming's left-hand rule. Force on a Current-Carrying Conductor
Direction: same direction attract, opposite repel. Force Between Two Parallel Currents
Torque is zero when $\vec{m}$ is parallel or anti-parallel to $\vec{B}$ . Torque on a Current Loop
For a solenoid, $m = N I A$ . Magnetic Moment
Radial field ensures torque is proportional to current (linear scale). Moving Coil Galvanometer
Shunt is in parallel, not series. Conversion of Galvanometer to Ammeter

Topics in Magnetic Effects of Current and Magnetism

Biot-Savart Law
Ampere's Law
Force on a Current
Moving Charge in a Magnetic Field
Magnetic Dipole
Magnetism and Matter

Previous-year questions on Magnetic Effects of Current and Magnetism

JEEGenie has 411 previous-year questions on Magnetic Effects of Current and Magnetism. A few worked examples follow.

Year	Questions
2026	19
2025	22
2024	34
2023	33
2022	29
2021	25
2020	21
2019	61
2018	10
2017	12
2016	5
2015	14
2014	8
2013	10
2012	12
2011	3
2010	3
2009	4
2008	3
2007	7
2006	4
2005	5
2004	6
2003	7
2002	9
2001	4
2000	4
1999	2
1998	4
1997	3
1996	2
1995	1
1994	1
1993	2
1992	1
1991	2
1990	2
1989	1
1988	3
1987	2
1986	1
1985	2
1984	2
1983	3
1982	1
1981	2

Question 1 easy

A solenoid having area A and length '

l

' is filled with a material having relative permeability 2. The magnetic energy stored in the solenoid is :

$\frac{B^{2} A l}{4 μ_{0}}$
$\frac{B^{2} A l}{2 μ_{0}}$
$\frac{B^{2} A l}{μ_{0}}$
$B^{2} A l$

Answer: A

Explanation. Energy density in a magnetic material is

u = \frac{B^{2}}{2 μ}

, where

μ = μ_{0} μ_{r}

. Given

μ_{r} = 2

, so

μ = 2 μ_{0}

. Thus

u = \frac{B^{2}}{2 (2 μ_{0})} = \frac{B^{2}}{4 μ_{0}}

. Volume of solenoid is

V = A l

. Total energy

U = u \cdot V = \frac{B^{2}}{4 μ_{0}} \cdot A l = \frac{B^{2} A l}{4 μ_{0}}

. The answer is option A.

From NTA/IIT papers: JEE Main 2025 · 2 Apr Shift 2

Question 2 hard

An infinitely long wire, located on the

z

-axis, carries a current

I

along the

+ z

-direction and produces the magnetic field

\vec{B}

. The magnitude of the line integral

\int \vec{B} \cdot \vec{d l}

along a straight line from the point

(- \sqrt{3} a, a, 0)

(a, a, 0)

is given by [

μ_{0}

is the magnetic permeability of free space.]

$7 μ_{0} I / 24$
$7 μ_{0} I / 12$
$μ_{0} I / 8$
$μ_{0} I / 6$

Answer: A

Explanation. For a long straight wire along the

z

-axis, the magnetic field is

\vec{B} = \frac{μ_{0} I}{2 π r} \hat{ϕ},

where

r

is the perpendicular distance from the

z

-axis and

\hat{ϕ}

is the azimuthal direction. The line integral along a straight path from

(- \sqrt{3} a, a, 0)

(a, a, 0)

lies in the plane

y = a

. Parametrize the path:

\vec{r} (t) = (- \sqrt{3} a + t (\sqrt{3} a + a), a, 0), 0 \leq t \leq 1.

x = - \sqrt{3} a + (\sqrt{3} + 1) a t

y = a

z = 0

. Then

r = \sqrt{x^{2} + a^{2}}

, and

\vec{d l} = ((\sqrt{3} + 1) a d t, 0, 0) .

The field at a point

(x, a, 0)

\vec{B} = \frac{μ_{0} I}{2 π (x^{2} + a^{2})} (- a \hat{x} + x \hat{y}),

since

\hat{ϕ} = (- y / r, x / r, 0)

with

y = a

. Thus

\vec{B} \cdot \vec{d l} = \frac{μ_{0} I}{2 π (x^{2} + a^{2})} (- a) \cdot ((\sqrt{3} + 1) a d t) = - \frac{μ_{0} I a^{2} (\sqrt{3} + 1)}{2 π (x^{2} + a^{2})} d t .

Change variable to

x

d x = (\sqrt{3} + 1) a d t \Rightarrow d t = \frac{d x}{(\sqrt{3} + 1) a} .

\vec{B} \cdot \vec{d l} = - \frac{μ_{0} I a}{2 π (x^{2} + a^{2})} d x .

Integrate from

x = - \sqrt{3} a

x = a

\int \vec{B} \cdot \vec{d l} = - \frac{μ_{0} I a}{2 π} \int_{- \sqrt{3} a}^{a} \frac{d x}{x^{2} + a^{2}} = - \frac{μ_{0} I}{2 π} {[\tan^{- 1} \frac{x}{a}]}_{- \sqrt{3} a}^{a} .

= - \frac{μ_{0} I}{2 π} (\tan^{- 1} (1) - \tan^{- 1} (- \sqrt{3})) = - \frac{μ_{0} I}{2 π} (\frac{π}{4} + \frac{π}{3}) = - \frac{μ_{0} I}{2 π} \cdot \frac{7 π}{12} = - \frac{7 μ_{0} I}{24} .

Magnitude is

\frac{7 μ_{0} I}{24} .

**Answer: A**

From NTA/IIT papers: JEE Advanced 2024

Question 3 medium

A proton, a deutron and an

α

-particle with same kinetic energy enter into a uniform magnetic field at right angle to magnetic field. The ratio of the radii of their respective circular paths is :

1 : $\sqrt{2}$ : $\sqrt{2}$
1 : 1 : $\sqrt{2}$
$\sqrt{2}$ : 1 : 1
1 : $\sqrt{2}$ : 1

Answer: D

Explanation. r = mv/qB = sqrt(2mK)/qB. Ratio: 1:sqrt(2):1

From NTA/IIT papers: JEE Main 2022 · 24 Jun Shift 2

Frequently asked questions

How much of JEE Main comes from Magnetic Effects of Current and Magnetism?: JEEGenie estimates about 5% of JEE Main marks come from Magnetic Effects of Current and Magnetism, based on recent papers. The share varies from year to year.
Which formulas matter most in Magnetic Effects of Current and Magnetism?: The Magnetic Effects of Current and Magnetism sheet on this page has 23 formula entries, starting with Biot-Savart Law, Magnetic Field Due to a Straight Current-Carrying Wire, Magnetic Field on Axis of a Circular Loop, Ampere's Circuital Law, Magnetic Field Inside a Solenoid. Each one comes with when to use it and the trap to avoid.
What topics does Magnetic Effects of Current and Magnetism cover for JEE?: Magnetic Effects of Current and Magnetism covers Biot-Savart Law, Ampere's Law, Force on a Current, Moving Charge in a Magnetic Field, Magnetic Dipole, Magnetism and Matter.
How should I revise Magnetic Effects of Current and Magnetism before the exam?: Learn each formula together with its condition of use, read the trap listed beside it, then practise questions and review every mistake. The practice link on this page opens Magnetic Effects of Current and Magnetism questions on JEEGenie.
How many previous-year questions are there on Magnetic Effects of Current and Magnetism?: JEEGenie has 411 previous-year questions on Magnetic Effects of Current and Magnetism, and this page shows a few with worked explanations.
Is practice on Magnetic Effects of Current and Magnetism free on JEEGenie?: Sign-up is free and includes a 7-day Pro trial. After the trial, free accounts keep a limited daily quota.