Magnetic Effects of Current — JEE Main PYQs

An electron gun is placed inside a long solenoid of radius $R$ on its axis. The solenoid has $n$ turns/length and carries a current I. The electron gun shoots an electron along the radius of the solenoid with speed v. If the electron does not hit the surface of the solenoid, maxi …

A long, straight wire of radius a carries a current distributed uniformly over its crosssection. The ratio of the magnetic fields due to the wire at distance $\frac{\mathrm{a}}{3}$ and 2 a , respectively from the axis of the wire is:

A charged particle of mass '$m$' and charge '$q$' moving under the influence of uniform electric field $E\vec{i}$ and a uniform magnetic field $\mathrm{B}\overrightarrow{\mathrm{k}}$ follows a trajectory from point $P$ to $Q$ as shown in figure. The velocities at $P$ and $Q$ ar …

A charged particle carrying charge $1\mu$C is moving with velocity $(2\hat{i}+3\hat{j}+4\hat{k})$ ms${}^{-1}$. If an external magnetic field of $(5\hat{i}+3\hat{j}-6\hat{k})\times 10^{-3}$ T exists in the region where the particle is moving then the force on the particle …

Magnitude of magnetic field (in SI units) at the centre of a hexagonal shape coil of side 10 cm, 50 turns and carrying current I (Ampere) in units of $\frac{{\mu }_0\mathrm{I}}{\pi }$ is:

A galvanometer coil has 500 turns and each turn has an average area of $3\times 10^{-4}{\mathrm{m}}^2$. If a torque of 1.5 Nm is required to keep this coil parallel to a magnetic field when a current of 0.5 A is flowing through it, the strength of the field (in T) is ______.

A charged particle going around in a circle can be considered to be a current loop. A particle of mass $m$ carrying charge $q$ is moving in a plane with speed $v$ under the influence of magnetic field $\vec{B}$. The magnetic moment of this moving particle:

A square loop of side 2 a and carrying current I is kept in $xz$ plane with its centre at origin. A long wire carrying the same current I is placed parallel to z -axis and passing through point ( $0,b,0$ ), ( $b\gg a$ ). The magnitude of torque on the loop about $z$-axis will …

A square loop of side 2a, and carrying current I , is kept in XZ plane with its centre at origin. A long wire carrying the same current I is placed parallel to the z -axis and passing through the point $(0,b,0),(b\gg a)$. The magnitude of the torque on the loop about z - axis …

A particle of charge $q$ and mass $m$ is moving with a velocity $-v\hat{i}(v\ne 0)$ towards a large screen placed in the $Y-Z$ plane at a distance $d$. If there is a magnetic field $\vec{B}=B_0\hat{k}$, the maximum value of $v$ for which the particle will not …

An electron is moving along $+x$ direction with a velocity of $6\times 10^6{\mathrm{ms}}^{-1}$. It enters a region of uniform electric field of $300\mathrm{V}/\mathrm{cm}$ pointing along +y direction. The magnitude and direction of the magnetic field set up in this r …

A wire A, bent in the shape of an arc of a circle, carrying a current of 2 A and having radius 2 cm and another wire B, also bent in the shape of arc of a circle, carrying a current of 3 A and having radius of 4 cm , are placed as shown in the figure. The ratio of the magnetic fi …

A circular coil having $N$ turns and radius $r$ carries a current. It is held in the $XZ$ plane in a magnetic field $B\hat{i}$. The torque on the coil due to the magnetic field is:

Two magnetic dipoles X and Y are placed at a separation $d$, with their axes perpendicular to each other. The dipole moment of Y is twice that of X. A particle of charge $q$ is passing through their mid-point P, at angle $\theta =45^{\circ }$ with the horizontal line as shown in th …

Two very long, straight and insulated wires are kept at $90^{\circ }$ angle from each other in xy plane as shown in the figure.

These wires carry current of equal magnitude I, whose directions are shown in the figure. The net magnetic field at point P will be:

A rigid square loop of side ' a ' and carrying current ${\mathrm{I}}_2$ is laying on a horizontal surface near a long current ${\mathrm{I}}_1$ wire in the same plane as shown in figure. The net force on the loop due to the wire will be:

An insulating thin rod of length $\ell$ has a linear charge density $\rho (x)={\rho }_0\frac{x}{\ell }$ on it. The rod is rotated about an axis passing through the origin ( $x=0$ ) and perpendicular to the rod. If the rod makes $n$ rotations per second, then the time averaged magne …

A thin ring of 10 cm radius carries a uniformly distributed charge. The ring rotates at a constant angular speed of $40\pi \mathrm{rad}{\mathrm{s}}^{-1}$ about its axis, perpendicular to its plane. If the magnetic field at its centre is $3.8\times 10^{-9}\mathrm{T}$, then …

The magnitude of the magnetic field at the centre of an equilateral triangular loop of side 1 m which is carrying a current of 10 A is: [Take ${\mu }_0=4\pi \times 10^{-7}{\mathrm{NA}}^{-2}$]

A square loop is carrying a steady current I and the magnitude of its magnetic dipole moment is m . If this square loop is changed to a circular loop and it carries the same current, the magnitude of the magnetic dipole moment of circular loop will be

In an experiment, electrons are accelerated, from rest, by applying, a voltage of 500 V . Calculate the radius of the path if a magnetic field 100 mT is then applied. [Charge of the electron $=1.6\times 10^{-19}\mathrm{C}$ Mass of the electron …

As shown in the figure, two infinitely long, identical wires are bent by $90^{\circ }$ and placed in such a way that the segments LP and QM are along the x-axis, while segments PS and QN are parallel to the $y$-axis. If $OP=OQ=4\mathrm{cm}$, and the magnitude of the magn …

A proton and an $\alpha$-particle (with their masses in the ratio of $1:4$ and charges in the ratio of $1:2$ are accelerated from rest through a potential difference V . If a uniform magnetic field (B) is set up perpendicular to their velocities, the ratio of the radii …

An electron, moving along the $x$-axis with an initial energy of 100 eV , enters a region of magnetic field $\vec{B}=\left(1.5\times 10^{-3}T\right)\hat{k}$ at $S$ (See figure). The field extends between $x=0$ and $x=2\mathrm{cm}$. The electron is detected at the point $Q$ o …

Find the magnetic field at point P due to a straight line segment AB of length 6 cm carrying a current of 5 A . (See figure)
( $\mu 0=4\mathrm{p}\times 10-7\mathrm{N}-\mathrm{A}-2$ )

A moving coil galvanometer has a coil with 175 turns and area $1{\mathrm{cm}}^2$ It uses a torsion band of torsion constant $10^{-6}\mathrm{N}-\mathrm{m}/\mathrm{rad}$. The coil is placed in a magnetic field B parallel to its plane. The coil deflects by $1^0$ for a curren …

A particle having the same charge as of electron moves in a circular path of radius 0.5 cm under the influence of a magnetic field of 0.5 T. If an electric field of $100\mathrm{V}/\mathrm{m}$ makes it to move in a straight path, then the mass of the particle is (given charge …

One of the two identical conducing wires of length $L$ is bent in the form of a circular loop and the other one into a circular coil of $N$ identical turns. If the same current is passed in both, the ratio of the magnetic field at the central of the loop …

A current loop, having two circular arcs joined by two radial lines is shown in the figure. It carries a current of 10 A. The magnetic field at point O will be close to:

An infinitely long current carrying wire and a small current carrying loop are in the plane of the paper as shown. the radius of the loop is a and distance of its centre from the wire is $\mathrm{d}(\mathrm{d}\gg \mathrm{a})$. If the loop applies a force $F$ on the wire then …

Two wires $A$ and $B$ are carrying currents $I_1$ and $I_2$ as shown in the figure. The separation between them is d . A third wire C carrying a current I is to be kept parallel to them at a distance x from A such that the net force acting on it is zero. The possible values o …

A proton, an electron, and a Helium nucleus, have the same energy. They are in circular orbitals in a plane due to magnetic field perpendicular to the plane. Let $r_p,r_e$ and $r_{He}$ be their respective radii, then,

The dipole moment of a circular loop carrying a current I, is m and the magnetic field at the centre of the loop is $B_1$. When the dipole moment is doubled by keeping the current constant, the magnetic field at the centre of the loop is $B_2$. The ratio $\frac{B_1}{B_2}$ is:

An electron, a proton and an alpha particle having the same kinetic energy are moving in circular orbits of radii $r_e$, $r_p$, $r_{\alpha }$ respectively in a uniform magnetic field $B$. The relation between $r_e$, $r_p$, $r_{\alpha }$ is:

Two identical wires A and B, each of length '$\ell$', carry the same current I. Wire A is bent into a circle of radius $R$ and wire B is bent to form a square of side 'a'. If $B_A$ and $B_B$ are the values of magnetic field at the centres of the circle and square respectively …

Two coaxial solenoids of different radii carry current I in the same direction. Let ${\overrightarrow{\mathrm{F}}}_1$ be the magnetic force on the inner solenoid due to the outer one and ${\overrightarrow{\mathrm{F}}}_2$ be the magnetic force on the outer solenoid due to the inne …

A rectangular loop of sides 10 cm and 5 cm carrying a current I of 12 A is placed in different orientations as shown in the figures below:

If there is a uniform magnetic field of 0.3 T in the positive z direction, in which orientations the loop would be in (i) stable equilibrium …

Two long current carrying thin wires, both with current I, are held by insulating threads of length L and are in equilibrium as shown in the figure, with threads making an angle '$\theta$' with the vertical. If wires have mass $\lambda$ per unit length then the value of I is: ( …

A charge Q is uniformly distributed over the surface of non conducting disc of radius R. The disc rotates about an axis perpendicular to its plane and passing through its centre with an angular velocity $\omega$. As a result of this rotation a magnetic field of induction B is obt …

Proton, Deuteron and alpha particle of the same kinetic energy are moving in circular trajectories in a constant magnetic field. The radii of proton, deuteron and alpha particle are respectively $r_p,r_d$ and $r_{\alpha }$. Which one of the following relations is correct?

A current I flows in an infinitely long wire with cross section in the form of a semicircular ring of radius R. The magnitude of the magnetic induction along its axis is

Two long parallel wires are at a distance 2d apart. They carry steady equal current flowing out of the plane of the paper as shown. The variation of the magnetic field along the line $XX$ ' is given by

A current loop ABCD is held fixed on the plane of the paper as shown in the figure. The arcs $BC$ (radius $=b$ ) and $DA$ (radius $=a$ ) of the loop are joined by two straight wires AB and CD . A steady current I is flowing in the loop. Angle made by AB and CD at the or …

A horizontal overhead power line is at a height of 4 m from the ground and carries a current of 100 A from east to west. The magnetic field directly below it on the ground is (${\mu }_0=4\pi \times 10^{-7}\mathrm{T}\mathrm{m}{\mathrm{A}}^{-1}$)

A long straight wire of radius 'a' carries a steady current i. The current is uniformly distributed across its cross section. The ratio of the magnetic field at $\frac{a}{2}$ and 2a is

A current I flows along the length of an infinitely long, straight, thin walled pipe. Then

A charged particle moves through a magnetic field perpendicular to its direction. Then

Two identical conducting wires AOB and COD are placed at right angles to each other. The wire AOB carries an electric current $I_1$ and COD carries a current $I_2$. The magnetic field on a point lying at a distance '$d$' from $O$, in a direction perpendicular to the plane of …

A charged particle with charge q enters a region of constant, uniform and mutually orthogonal fields $\vec{E}$ and $\vec{B}$ with a velocity $\vec{v}$ perpendicular to both $\vec{E}$ and $\vec{B}$, and comes out without any change in magnitude or direction of $\vec{v}$. Then

In a region, steady and uniform electric and magnetic fields are present. These two fields are parallel to each other. A charged particle is released from rest in this region. The path of the particle will be a