Magnetism

In a vacuum chamber, a particle of charge $1\ \mu C$ and mass $1\ \mathrm{mg}$ 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 $1\hat{i}\ \mathrm{Vm}^{-1}$. A...

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 ...

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 t...

A positive, singly ionized atom of mass number $A_{\mathrm{M}}$ is accelerated from rest by the voltage $192 \mathrm{~V}$. Thereafter, it enters a rectangular region of width $w$ with magnetic field $\vec{B}_0=0.1 \hat{k}$ Tesla, as shown i...

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 show...

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 $\int \vec{B} \cdot \overrightarrow{d l}$ along a straight line f...

A rectangular conducting loop of length $4 \mathrm{~cm}$ and width $2 \mathrm{~cm}$ is in the $x y$-plane, as shown in the figure. It is being moved away from a thin and long conducting wire along the direction $\frac{\sqrt{3}}{2} \hat{x}+\...

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

A small circular loop of area $A$ and resistance $R$ is fixed on a horizontal $x y$-plane with the center of the loop always on the axis $\hat{n}$ of a long solenoid. The solenoid has $m$ turns per unit length and carries current $I$ counte...

The work done in bringing the dipole from infinity to a distance r from the center of the loop by the given process is proportional to

When the dipole m is placed at a distance r from the center of the loop (as shown in the figure), the current induced in the loop will be proportional to

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 I1 in the anti-clockwise direction and the large...

An \(\alpha\)-particle (mass 4 amu) and a singly charged sulphur 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 vel...

A long straight wire carries a current, I = 2 ampere. A semi-circular conducting rod is placed beside it on two conducting parallel rails of negligible resistance. Both the rails are parallel to the wire. The wire, the rod and the rails lie...

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 capaci...

A light disc made of aluminium (a nonmagnetic material) is kept horizontally and is free to rotate
about its axis as shown in the figure. A strong magnet is held vertically at a point above the disc away
from its axis. On revolving the magn...

A moving coil galvanometer has \(50\) turns and each turn has an area \(2 \times {10^{ - 4}}\,{m^2}.\) The magnetic field produced by the magnet inside the galvanometer is \(0.02\) \(T.\) The torsional constant of the suspension wire is $${...

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 circul...

In the \(xy\)-plane, the region \(y > 0\) has a uniform magnetic field \({B_1}\widehat k\) and the region \(y < 0\) has another uniform magnetic field \({B_2}\widehat k.\) A positively charged particle is projected from the origin along the...

A uniform magnetic field \(B\) exist in the region between \(x=0\) and \(x = {{3R} \over 2}\) (region \(2\) in the figure) pointing normally into the plane of the paper. A particle with charge \(+Q\) and momentum \(p\) directed along \(x\)-...

A symmetric star shaped conducting wire loop is carrying a steady state current \({\rm I}\) 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 c...

In which case will the particle describe a helical path with axis along the positive \(z\) direction?

In which case would the particle move in a straight line along the negative direction of \(y\)-axis (i.e., move along \(- \widehat y\))?

In which case will the particle move in a straight line with constant velocity?

Consider two different metallic strips (1 and 2) of the same material. Their lengths are the same, widths are w1 and w2 and thickness are d1 and d2, respectively. Two points K and M are symmetrically located on the opposite faces parallel t...

Consider two different metallic strips (1 and 2) of same dimensions (length l, width w and thickness d) with carrier densities n1 and n2, respectively. Strip 1 is placed in magnetic field B1 and strip 2 is placed in magnetic field B2, both ...

A conductor (shown in the figure) carrying constant current I is kept in the x-y plane in a uniform magnetic field B. If F is the magnitude of the total magnetic force acting on the conductor, then the correct statements is/are

Consider d >> a, and the loop is rotated about its diameter parallel to the wires by 30\(^\circ\) from the position shown in the below figure. If the currents in the wires are in the opposite directions, the torque on the loop at its new po...

When d \(\approx\) a but wires are not touching the loop, it is found that the net magnetic field on the axis of the loop is zero at a height h above the loop. In that case

Two parallel wires in the plane of the paper are distance X0 apart. A point charge is moving with speed u between the wires in the same plane at a distance X1 from one of the wires. When the wires carry current of magnitude I in the same di...

The change in the magnetic dipole moment associated with the orbit, at the end of the time interval of the magnetic field change, is

The magnitude of the induced electric field in the orbit at any instant of time during the time interval of the magnetic field change is

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....

A particle of mass M and positive charge Q, moving with a constant velocity \({\overrightarrow u _1} = 4\widehat i\) ms\(-\)1 enters a region of uniform static magnetic field, normal to the xy plane. The region of the magnetic field extends...

An infinite 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, \(\left| {\overrightarrow B } \right|\) as a function of the radia...

A loop carrying current \(l\) lies in the xy-plane as shown in the figure. The unit vector \(\widehat k\) is coming out of the plane of the paper. The magnetic moment of the current loop is

A cylinder 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...

Consider the motion of a positive point charge in a region, there are simultaneous uniform electric and magnetic fields \(\overrightarrow E = {E_0}\widehat j\) and \(\overrightarrow B = {B_0}\widehat j\). At time t = 0, this charge has ve...

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 xy-plane and a steady current I flows through the wire. The z-component of the magnetic field at ...

A dense collection of equal number of electrons and positive ions is called neutral plasma. Certain solids containing
fixed positive ions surrounded by free electrons can be treated as neutral plasma. Let 'N' be the number density of
free e...

A long circular tube of length 10 m and radius 0.3 m carries a current I along its curved surface as shown. A wire-loop of resistance 0.005 \(\Omega\) and of radius 0.1 m is placed inside the tube with its axis coinciding with the axis of t...

An electron and a proton are moving on straight parallel paths with same velocity. They enter a semi-infinite region of uniform magnetic field perpendicular to the velocity. Which of the following statement(s) is/are true?

A superconductor has Tc(0) = 100 K. When a magnetic field of 7.5 T is applied, its Tc decreases to 75 K. For this material, one can definitely say that when

In the graph below, the resistance R of a superconductor is shown as a friction of its temperature T for two different magnetic fields B1 (solid line) and B2 (dashed line). If B2 is larger than B1 which of the following graphs shows the cor...

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 ...

A steady current I goes through a wire loop PQR having shape of a right angle triangle with PQ = 3x, PR = 4x and QR = 5x. If the magnitude of the magnetic field at P due to this loop is \(k\left( {{{{\mu _0}I} \over {48\pi x}}} \right)\), f...

STATEMENT 1 : The sensitivity of a moving coil galvanometer is increased by placing a suitable magnetic material as a core inside the coil.
and
STATEMENT 2 : Soft iron has a high magnetic permeability and cannot be easily magnetized or dema...

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 \(l\)...

Two wires each carrying a steady current I are shown in four configurations in Column I. Some of the resulting effects are described in Column II. Match the statements in Column I with the statements in Column II and indicate your answer by...

A magnetic field \(\overrightarrow{\mathrm{B}}=\mathrm{B}_{0} \hat{j}\) exists in the region \(a < x < 2 a\) and \(\overrightarrow{\mathrm{B}}=-\mathrm{B}_{0} \hat{j}\), in the region \(2 a < x < 3 a\), where \(\mathrm{B}_{0}\) is a positiv...