Magnetic Effect of Electric Current Class 12 - IIT JEE | NEET

Team eSaral

eSaral Academic and Editorial Team

13th November 2026

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Summary

The magnetic effect of electric current is the magnetic field that a current produces around a conductor. These Class 12 notes cover Oersted's experiment, the Biot-Savart law, the field of a wire, a loop and a solenoid, the Lorentz force and the motion of a charge in a magnetic field, the force on a conductor, the torque on a current loop and the moving coil galvanometer, with formulas, solved examples and FAQs for boards, JEE and NEET.

Magnetic Effect of Electric Current Class 12

The magnetic effect of electric current is the first topic of the NCERT Class 12 chapter Moving Charges and Magnetism (Chapter 4), and it connects electricity and magnetism. This page is the chapter overview: the main ideas and formulas in one place, with links to eSaral's pages on each topic, such as Biot-Savart law and the introduction, the applications of Ampere's law and the magnetic field of a solenoid.

What Is the Magnetic Effect of Electric Current?

When an electric current flows through a conductor, it produces a magnetic field around it. Hans Christian Oersted discovered this in 1820, when he saw a compass needle deflect near a wire that carried a current. It showed that moving charges are a source of a magnetic field, while a static charge is not.

The field lines of a long straight wire are concentric circles around the wire.
Right-hand thumb rule: hold the wire in the right hand with the thumb along the current, and the curled fingers show the direction of the field.
The unit of the magnetic field is the tesla (T), and $\mu_0 = 4\pi\times 10^{-7}\ \text{T m/A}$.

Handwritten Notes on the Magnetic Effect of Electric Current

These are eSaral's handwritten Class 12 notes on the chapter, as images.

India's Best Exam Preparation for Class 12th - Download Now

Magnetic Effect of Electric Current: Formulas at a Glance

Topic	Formula
Biot-Savart law	$dB = \dfrac{\mu_0}{4\pi}\dfrac{I\,d\ell\sin\theta}{r^2}$
Infinite straight wire	$B = \dfrac{\mu_0 I}{2\pi d}$
Finite straight wire	$B = \dfrac{\mu_0 I}{4\pi d}(\sin\phi_1 + \sin\phi_2)$
Centre of a circular loop ($N$ turns)	$B = \dfrac{\mu_0 NI}{2R}$
Axis of a circular loop	$B = \dfrac{\mu_0 N I R^2}{2(R^2 + x^2)^{3/2}}$
Arc of angle $\theta$ at its centre	$B = \dfrac{\mu_0 I\theta}{4\pi R}$
Long solenoid, toroid	$B = \mu_0 nI$, $\ B = \dfrac{\mu_0 NI}{2\pi r}$
Lorentz force	$\vec{F} = q(\vec{E} + \vec{v}\times\vec{B})$
Charge in a magnetic field ($v \perp B$)	$r = \dfrac{mv}{qB}$, $\ T = \dfrac{2\pi m}{qB}$
Force on a conductor	$\vec{F} = I\,\vec{\ell}\times\vec{B}$, magnitude $BI\ell\sin\theta$
Force between parallel wires	$\dfrac{F}{l} = \dfrac{\mu_0 I_1 I_2}{2\pi d}$
Torque on a current loop	$\vec{\tau} = \vec{m}\times\vec{B}$, $\ \tau = NIAB\sin\theta$

Magnetic Effect of Electric Current: Biot-Savart Law

The Biot-Savart law gives the magnetic field $d\vec{B}$ at a point P due to a small current element $I\,d\vec{\ell}$ at a distance $r$:

$$d\vec{B} = \frac{\mu_0}{4\pi}\,\frac{I\,d\vec{\ell}\times\hat{r}}{r^2}$$

The direction of $d\vec{B}$ is perpendicular to the plane of $d\vec{\ell}$ and $\vec{r}$, and it is given by the right-hand rule.
The field is zero along the line of the element ($\theta = 0^\circ$) and maximum at $\theta = 90^\circ$.
It is the magnetic equivalent of Coulomb's law, but the field depends on the angle, and there is no field along the current.

Magnetic Effect of Electric Current: Field of a Wire, a Loop and an Arc

Straight wire. For a wire of any length, with the angles $\phi_1$ and $\phi_2$ measured from the perpendicular to the ends,

$$B = \frac{\mu_0 I}{4\pi d}(\sin\phi_1 + \sin\phi_2)$$

For an infinite wire, $\phi_1 = \phi_2 = 90^\circ$, so $B = \dfrac{\mu_0 I}{2\pi d}$.

Circular loop. Every element of the loop is at the same distance $R$ from the centre and is perpendicular to the line joining it to the centre, so at the centre

$$B = \frac{\mu_0 NI}{2R}$$

For a semicircle, $B = \dfrac{\mu_0 I}{4R}$, and for an arc that subtends an angle $\theta$ at the centre, $B = \dfrac{\mu_0 I\theta}{4\pi R}$.

Magnetic Effect of Electric Current: Ampere's Law, Solenoid and Toroid

Ampere's circuital law, $\oint \vec{B}\cdot d\vec{\ell} = \mu_0 I_{enc}$, gives the field of symmetric currents quickly. The results are $B = \mu_0 nI$ inside a long solenoid and $B = \dfrac{\mu_0 NI}{2\pi r}$ inside a toroid. The full derivations, with the solid and hollow cylinders, are in eSaral's applications of Ampere's law and magnetic field of a solenoid pages.

Magnetic Effect of Electric Current: Force on a Moving Charge (Lorentz Force)

A charge $q$ moving with velocity $\vec{v}$ in a magnetic field $\vec{B}$ experiences a force

$$\vec{F} = q(\vec{v}\times\vec{B}), \qquad F = qvB\sin\theta$$

The force is perpendicular to both $\vec{v}$ and $\vec{B}$, so it does no work, and it does not change the speed.

$\vec{v}\perp\vec{B}$: circular path, with $r = \dfrac{mv}{qB}$ and $T = \dfrac{2\pi m}{qB}$.
$\vec{v}$ oblique to $\vec{B}$: helical path, with radius $\dfrac{mv\sin\theta}{qB}$ and pitch $\dfrac{2\pi m v\cos\theta}{qB}$.
$\vec{v}\parallel\vec{B}$: straight path, because $F = 0$.
Velocity selector: with perpendicular $\vec{E}$ and $\vec{B}$, a charge moves undeflected if $v = \dfrac{E}{B}$.

Motion of a charged particle in a uniform magnetic field

Magnetic Effect of Electric Current: Force on a Conductor and Between Parallel Wires

A conductor of length $\ell$ that carries a current $I$ in a field $\vec{B}$ feels a force

$$\vec{F} = I\,\vec{\ell}\times\vec{B}, \qquad F = BI\ell\sin\theta$$

Two long parallel wires with currents $I_1$ and $I_2$ at a distance $d$ exert a force per unit length

$$\frac{F}{l} = \frac{\mu_0 I_1 I_2}{2\pi d}$$

The wires attract each other if the currents are in the same direction, and repel each other if they are opposite. This defines the ampere: 1 A is the current for which the force is $2\times 10^{-7}$ N per metre of two long parallel wires 1 m apart in vacuum.

Magnetic Effect of Electric Current: Torque on a Loop and the Galvanometer

A coil of $N$ turns, area $A$ and current $I$ has a magnetic moment $\vec{m} = NI\vec{A}$. In a field $\vec{B}$, it experiences a torque

$$\vec{\tau} = \vec{m}\times\vec{B}, \qquad \tau = NIAB\sin\theta$$

where $\theta$ is the angle between $\vec{m}$ (the normal to the coil) and $\vec{B}$. This is the principle of the moving coil galvanometer, in which a radial field keeps the torque equal to $NIAB$ in every position of the coil.

Current sensitivity: $\dfrac{\theta}{I} = \dfrac{NAB}{k}$
Voltage sensitivity: $\dfrac{\theta}{V} = \dfrac{NAB}{kR}$
Ammeter: a shunt $S = \dfrac{I_g G}{I - I_g}$ in parallel
Voltmeter: a resistance $R = \dfrac{V}{I_g} - G$ in series

See eSaral's moving coil galvanometer page for the construction and the working.

Solved Examples on the Magnetic Effect of Electric Current

Example 1: Field at the centre of a loop

A circular coil of 100 turns and radius 5 cm carries a current of 0.5 A. Find the magnetic field at its centre.

$$B = \frac{\mu_0 NI}{2R} = \frac{4\pi\times 10^{-7}\times 100\times 0.5}{2\times 0.05} \approx 6.28\times 10^{-4}\ \text{T}$$

Example 2: Radius of the path of an electron

An electron moves at $2\times 10^6$ m/s perpendicular to a field of 0.01 T. Find the radius of its path. ($m = 9.1\times 10^{-31}$ kg, $e = 1.6\times 10^{-19}$ C)

$$r = \frac{mv}{eB} = \frac{9.1\times 10^{-31}\times 2\times 10^6}{1.6\times 10^{-19}\times 0.01} \approx 1.14\times 10^{-3}\ \text{m} = 1.14\ \text{mm}$$

Example 3: Force between two wires

Two long parallel wires carry 10 A and 20 A in the same direction, 5 cm apart. Find the force per unit length.

$$\frac{F}{l} = \frac{\mu_0 I_1 I_2}{2\pi d} = \frac{2\times 10^{-7}\times 10\times 20}{0.05} = 8\times 10^{-4}\ \text{N/m (attractive)}$$

Example 4: Torque on a coil

A coil of 50 turns and area $0.02\ \text{m}^2$ carries 2 A in a field of 0.5 T, with its plane parallel to the field. Find the torque.

For the plane parallel to the field, the normal is perpendicular to $\vec{B}$, so $\sin\theta = 1$:

$$\tau = NIAB = 50\times 2\times 0.02\times 0.5 = 1\ \text{N m}$$

Example 5: Galvanometer to ammeter

A galvanometer of resistance 50 $\Omega$ gives a full-scale deflection for 5 mA. What shunt converts it into an ammeter of range 0 to 1 A?

$$S = \frac{I_g G}{I - I_g} = \frac{0.005\times 50}{1 - 0.005} \approx 0.25\ \Omega$$

Common Mistakes in the Magnetic Effect of Electric Current

Mistake	Correct approach
Using $\sin\theta = 1$ in the Biot-Savart law for every element	The angle is between $d\vec{\ell}$ and $\vec{r}$. For a straight wire, it changes along the wire
Using $\mu_0 I/2\pi d$ for a finite wire	That is only for an infinite wire. Use the $\sin\phi_1 + \sin\phi_2$ formula
Saying that the magnetic force changes the kinetic energy	It is perpendicular to $\vec{v}$, so it does no work
Thinking that the time period depends on the speed	$T = 2\pi m/qB$ is independent of $v$
Using the wrong angle in $\tau = NIAB\sin\theta$	$\theta$ is between the normal to the coil and $\vec{B}$, and not between the plane and $\vec{B}$
Using a series resistance for an ammeter	An ammeter needs a small shunt in parallel, and a voltmeter needs a large resistance in series

More on Moving Charges and Magnetism

For the complete Class 12 Physics notes, see eSaral's Class 12 Physics notes. Revise with the mind map of the magnetic effects of current, and practise with the important questions for Class 12 Physics Chapter 4.

Frequently Asked Questions

What is the magnetic effect of electric current?

The magnetic effect of electric current is the production of a magnetic field around a conductor when a current flows through it. Hans Christian Oersted observed it in 1820, when a compass needle near a current-carrying wire was deflected. The field gets stronger when the current is larger, and weaker as the distance from the wire increases.

What is the Biot-Savart law?

The Biot-Savart law gives the magnetic field of a small current element: $d\vec{B} = \dfrac{\mu_0}{4\pi}\dfrac{I\,d\vec{\ell}\times\hat{r}}{r^2}$, and in magnitude $dB = \dfrac{\mu_0}{4\pi}\dfrac{I\,d\ell\sin\theta}{r^2}$. It works for any shape of conductor, and the total field is found by integrating over the conductor.

What is the magnetic field at the centre of a circular current loop?

For a loop of radius $R$ with $N$ turns carrying a current $I$, the field at the centre is $B = \dfrac{\mu_0 NI}{2R}$. On the axis at a distance $x$ from the centre, $B = \dfrac{\mu_0 N I R^2}{2(R^2 + x^2)^{3/2}}$.

What is the difference between the Biot-Savart law and Ampere's circuital law?

The Biot-Savart law gives the field of a current element and works for any geometry, but it needs an integration. Ampere's circuital law relates $\oint \vec{B}\cdot d\vec{\ell}$ to the enclosed current, and it gives $B$ easily only for symmetric currents such as a long wire, a solenoid or a toroid. eSaral's page on the applications of Ampere's law has the derivations.

What is the Lorentz force, and what are the radius and time period of a charged particle in a magnetic field?

The Lorentz force is $\vec{F} = q(\vec{E} + \vec{v}\times\vec{B})$, and in a pure magnetic field it is $q\vec{v}\times\vec{B}$. For $\vec{v}\perp\vec{B}$, the path is a circle with radius $r = \dfrac{mv}{qB}$ and time period $T = \dfrac{2\pi m}{qB}$, which does not depend on the speed.

Why does a magnetic field do no work on a moving charge?

The magnetic force is always perpendicular to the velocity, so the work done is $\vec{F}\cdot d\vec{s} = 0$. It changes the direction of the velocity but not the speed, so the kinetic energy of the charge remains constant.

What is the force between two parallel current-carrying wires?

The force per unit length is $\dfrac{F}{l} = \dfrac{\mu_0 I_1 I_2}{2\pi d}$, attractive for currents in the same direction and repulsive for opposite currents. One ampere is the current that gives a force of $2\times 10^{-7}$ N per metre between two long parallel wires 1 m apart in vacuum.

How is a moving coil galvanometer converted into an ammeter and a voltmeter?

For an ammeter, a small shunt resistance $S = \dfrac{I_g G}{I - I_g}$ is connected in parallel. For a voltmeter, a large resistance $R = \dfrac{V}{I_g} - G$ is connected in series. Here $G$ is the resistance of the galvanometer, and $I_g$ is its full-scale current.

Is Moving Charges and Magnetism the same as the magnetic effect of electric current?

Yes. In the NCERT Class 12 Physics book, the magnetic effect of electric current is covered in Chapter 4, Moving Charges and Magnetism. It includes the Biot-Savart law, Ampere's law, the Lorentz force, the force on current-carrying conductors, the torque on a loop and the moving coil galvanometer.

How many questions come from the magnetic effect of electric current in JEE and NEET?

The chapter usually gives a few questions in JEE Main and NEET, but the number changes every year, so check the previous year questions for the pattern. The most tested ideas are the field of a wire and a loop, the motion of a charge in a magnetic field, and the force on a conductor. eSaral's chapter-wise PYQs and important questions help you to practise them.

Where can I find notes and questions on the magnetic effect of electric current?

eSaral has the Biot-Savart law introduction, the applications of Ampere's law, the solenoid derivation, the moving coil galvanometer page, the mind map and the important questions for Class 12 Physics Chapter 4. All of them are linked on this page.

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eSaral Academic and Editorial Team

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Magnetic Effect of Electric Current Class 12 - IIT JEE | NEET

Summary

What Is the Magnetic Effect of Electric Current?

Handwritten Notes on the Magnetic Effect of Electric Current

Magnetic Effect of Electric Current: Formulas at a Glance

Magnetic Effect of Electric Current: Biot-Savart Law

Magnetic Effect of Electric Current: Field of a Wire, a Loop and an Arc

Magnetic Effect of Electric Current: Ampere's Law, Solenoid and Toroid

Magnetic Effect of Electric Current: Force on a Moving Charge (Lorentz Force)

Magnetic Effect of Electric Current: Force on a Conductor and Between Parallel Wires

Magnetic Effect of Electric Current: Torque on a Loop and the Galvanometer

Solved Examples on the Magnetic Effect of Electric Current

Example 1: Field at the centre of a loop

Example 2: Radius of the path of an electron

Example 3: Force between two wires

Example 4: Torque on a coil

Example 5: Galvanometer to ammeter

Common Mistakes in the Magnetic Effect of Electric Current

More on Moving Charges and Magnetism

Frequently Asked Questions

Team eSaral

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