Magnetic Effects of Current — JEE Advanced PYQs

A hollow, right circular cone of base radius $R$ and height $h$, with its tip at the origin is rotating about the Z-axis with an angular velocity $\omega$, as shown in the figure. The cone carries a total charge Q uniformly distributed on its curved surface. The magnitude of magn …

In a vacuum chamber, a particle of charge $1\mu \mathrm{C}$ and mass 1 mg is projected with a velocity $(\hat{i}+2\hat{j}){\mathrm{ms}}^{-1}$ from the $XZ$ plane at time $t=0$ in an electric field of $1\hat{ı}{\mathrm{Vm}}^{-1}$. At $t=0.2\mathrm{s}$, the elec …

A conducting solid sphere of radius $R$ and mass $M$ carries a charge $Q$. The sphere is rotating about an axis passing through its center with a uniform angular speed $\omega$. The ratio of the magnitudes of the magnetic dipole moment to the angular momentum about the sa …

An infinitely long wire, located on the $z$-axis, carries a current $I$ along the +z-direction and produces the magnetic field $\overrightarrow{\mathrm{B}}$. The magnitude of the line integral $\int \overrightarrow{\mathrm{B}}.\overrightarrow{dl}$ along a straight line …

A thin stiff insulated metal wire is bent into a circular loop with its two ends extending tangentially from the same point of the loop. The wire loop has mass $m$ and radius $r$ and it is in a uniform vertical magnetic field $B_0$, as shown in the figure. Initially, it hangs v …

A positive, singly ionized atom of mass number $A_{\mathrm{M}}$ is accelerated from rest by the voltage 192 V. Thereafter, it enters a rectangular region of width $w$ with magnetic field ${\vec{B}}_0=0.1\hat{k}$ Tesla, as shown in the figure. The ion finally hits a detector at t …

Which one of the following options represents the magnetic field $\vec{B}$ at O due to the current flowing in the given wire segments lying on the $xy$ plane?

Two concentric circular loops, one of radius $R$ and the other of radius $2R$, lie in the $xy$-plane with the origin as their common center, as shown in the figure. The smaller loop carries current $I_1$ in the anti-clockwise direction and the larger loop carries curr …

An $\alpha$-particle (mass 4 amu) and a singly charged sulfur ion (mass 32 amu) are initially at rest. They are accelerated through a potential V and then allowed to pass into a region of uniform magnetic field which is normal to the velocities of the particles. Within this regio …

A circular coil of radius R and N turns has negligible resistance. As shown in the schematic figure, its two ends are connected to two wires and it is hanging by those wires with its plane being vertical. The wires are connected to a capacitor with charge Q through a switch. The …

Two infinitely long straight wires lie in the $xy$-plane along the lines $x=\pm R$. The wire located at $x=+R$ carries a constant current $I_1$ and the wire located at $x=-R$ carries a constant current $I_2$. A circular loop of radius $R$ is suspended with its centre at …

In the $xy$-plane, the region $y>0$ has a uniform magnetic field $B_1\hat{k}$ and the region $y<0$ has another uniform magnetic field $B_2\hat{k}$. A positively charged particle is projected from the origin along the positive $y$-axis with speed $v_0=\pi m{s}^{-1}$ …

A charged particle (electron or proton) is introduced at the origin $(x=0,y=0,z=0)$ with a given initial velocity $\vec{v}$. A uniform electric field $\vec{E}$ and a uniform magnetic field $\vec{B}$ exist everywhere. The velocity $\vec{v}$, electric field $\vec{E}$ …

A charged particle (electron or proton) is introduced at the origin $(x=0,y=0,z=0)$ with a given initial velocity $\vec{v}$. A uniform electric field $\vec{E}$ and a uniform magnetic field $\vec{B}$ exist everywhere. The velocity $\vec{v}$, electric field $\vec{E}$ …

A charged particle (electron or proton) is introduced at the origin $(x=0,y=0,z=0)$ with a given initial velocity $\vec{v}$. A uniform electric field $\vec{E}$ and a uniform magnetic field $\vec{B}$ exist everywhere. The velocity $\vec{v}$, electric field $\vec{E}$ …

A symmetric star shaped conducting wire loop is carrying a steady state current $I$ as shown in the figure. The distance between the diametrically opposite vertices of the star is $4a$. The magnitude of the magnetic field at the center of the loop is

A uniform magnetic field $B$ exists in the region between $x=0$ and $x=\frac{3R}{2}$ (region 2 in the figure) pointing normally into the plane of the paper. A particle with charge $+Q$ and momentum $p$ directed along $x$-axis enters region 2 from region 1 at point …

A conductor (shown in the figure) carrying contant current I is kept in the x-y plane in a uniform magnetic field $\vec{B}$. IF F is the magnitude of the total magnetic force acting on the conductor, then the correct statement(s) is (are):

PARAGRAPH 1

In a thin rectangular metallic strip a constant current I flows along the positive x-direction, as shown in the figure. The length, width and thickness of the strip are l, w and d, respectively.

A uniform magnetic field B is applied on the strip along the positive y …

PARAGRAPH 1

In a thin rectangular metallic strip a constant current I flows along the positive x-direction, as shown in the figure. The length, width and thickness of the strip are l, w and d, respectively.

A uniform magnetic field B is applied on the strip along the positive y …

The figure shows a circular loop of radius $a$ with two long parallel wires (numbered 1 and 2) all in the plane of the paper. The distance of each wire from the centre of the loop is $d$. The loop and the wires are carrying the same current $I$. The current in the loop is i …

The figure shows a circular loop of radius $a$ with two long parallel wires (numbered 1 and 2) all in the plane of the paper. The distance of each wire from the centre of the loop is $d$. The loop and the wires are carrying the same current $I$. The current in the loop is i …

Two parallel wires in the plane of the paper are distance $X_0$ apart. A point charge is moving with speed $u$ between the wires in the same plane at a distance $X_1$ from one of the wires. When the wires carry current of magnitude $I$ in the same direction, the radiu …

A particle of mass $M$ and positive charge $Q$, moving with a constant velocity ${\vec{u}}_1=4\hat{i}m{s}^{-1}$, enters a region of uniform static magnetic field normal to the $x-y$ plane. The region of the magnetic field extends from $x=0$ to $x=L$ for all values of …

A steady current $I$ flows along an infinitely long hollow cylindrical conductor of radius $R$. This cylinder is placed coaxially inside an infinite solenoid of radius $2R$. The solenoid has $n$ turns per unit length and carries a steady current $I$. Consider a point …

Consider the motion of a positive point charge in a region where there are simultaneous uniform electric and magnetic fields $\vec{E}=E_0\hat{j}$ and $\vec{B}=B_0\hat{j}$. At time $t=0$, this charge has velocity $\vec{v}$ in the $x-y$ plane, making an angle …

A cylindrical cavity of diameter $a$ exists inside a cylinder of diameter $2a$ as shown in the figure. Both the cylinder and the cavity are infinitely long. A uniform current density $J$ flows along the length. If the magnitude of the magnetic field at the point $P$ is g …

A loop carrying current $I$ lies in the $x-y$ plane as shown in the figure. The unit vector $\hat{k}$ is coming out of the plane of the paper. The magnetic moment of the current loop is

An infinitely long hollow conducting cylinder with inner radius $R/2$ and outer radius $R$ carries a uniform current density along its length. The magnitude of the magnetic field, $|\vec{B}|$ as a function of the radial distance $r$ from the axis is best represented by

A long insulated copper wire is closely wound as a spiral of ' $N$ ' turns. The spiral has inner radius ' $a$ ' and outer radius ' $b$ '. The spiral lies in the X-Y plane and a steady current ' $I$ ' flows through the wire. The Z-component of the magnetic field at the cen …

A thin flexible wire of length L is connected to two adjacent fixed points and carries a current I in the clockwise direction, as shown in the figure. When the system is put in a uniform magnetic field of strength B going into the plane of the paper, the wire takes the shape of a …

A steady current $I$ goes through a wire loop PQR having shape of a right angle triangle with $\mathrm{PQ}=3x,\mathrm{PR}=4x$ and $\mathrm{QR}=5x$. If the magnitude of the magnetic field at P due to this loop is $k\left(\frac{{\mu }_{0}I}{48\pi x}\right)$, find the val …

A particle of mass $m$ and charge $q$, moving with velocity $V$ enters Region II normal to the boundary as shown in the figure. Region II has a uniform magnetic field $B$ perpendicular to the plane of the paper. The length of the Region II is $\ell$. Choose the correct …

A magnetic field $\vec{B}=B_0\hat{j}$ exists in the region $a<x<2a$ and $\vec{B}=-B_0\hat{j}$, in the region $2a<x<3a$, where $B_0$ is a positive constant. A positive point charge moving with a velocity $\vec{v}=v_0\hat{i}$, where $v_0$ is a positive constant, ent …

An infinite current carrying wire passes through point O and in perpendicular to the plane containing a current carrying loop ABCD as shown in the figure. Choose the correct option (s).