Force on a Current-Carrying Conductor in a Magnetic Field.

A metal ring of radius r = 0.5 m with its plane normal to a uniform magnetic field B of induction 0.2 T carries a current I = 100 A. The tension in newtons developed in the ring is :

A semi circular current carrying wire having radius $R$ is placed in $\mathrm{x}-\mathrm{y}$ plane with its centre at origin $\mathrm{{\rm O}}$. There is non-uniform magnetic field $\overrightarrow{B}=\left(\frac{{\mathrm{B}}_{\mathrm{o}}\mathrm{x}}{\mathrm{2}\mathrm{R}}\right)\widehat{\mathrm{k}}$ $\left(\text{here}{B}_{\mathrm{o}} \text{is} +\text{ve constant}\right)$  is existing in the region. The magnetic force acting on semi-circular wire will be along:

A conducting wire bent in the form of a parabola ${\text{y}}^2=2\text{x}$  carries a current i = 2 A as shown in figure. This wire is placed in a uniform magnetic field $\overrightarrow{\text{B}}=-\text{4}\widehat{\text{k}}$ Tesla. The magnetic force on the wire is (in newton)

A straight rod of mass m and length $L$ is suspended from the identical spring as shown in the figure. The spring stretched by a distance of ${\mathit{\text{x}}}_0$ due to the weight of the wire. The circuit has total resistance $R \mathrm{\Omega }$. When the magnetic field perpendicular to the plane of the paper is switched on, springs are observed to extend further by the same distance. The magnetic field strength is

A long thin-walled pipe of radius $R$ carries a current $i$ along its length. The current density is uniform over the circumference of the pipe. The magnetic field at the centre of the pipe due to the quarter portion of the pipe shown, is

An infinite wire placed along $z$-axis, has current $I_1$ in positive $z$-direction. A conducting rod placed in $xy$ plane parallel to y-axis has current $I_2$ in positive y-direction. The ends of the rod subtend angles of $+30°$ and $-60°$ at the origin with positive $x$-direction. The rod is at a distance $a$ from the origin. Find net force on the rod.

A $U$ shaped wire of mass $m$ and length $l$ is immersed with its two ends in mercury (see figure). The wire is in a homogeneous field of magnetic induction $B$. If a charge, that is, a current pulse $q=\int i\mathrm{d}t,$sent through the wire, the wire will jump up. Calculate, from the height $h$ that the wire reaches, the size of the charge or current pulse, assuming that the time of the current pulse is very small in comparison with the time of flight. Make use of the fact that impulse of force equals $\int F\mathrm{d}t,$ which equals $mv$. Evaluate $q$ for following details:
$B=0.1 \mathrm{Wb} {\mathrm{m}}^{-2}\mathrm{,} m=10 \mathrm{g}\mathrm{,}l=20 \mathrm{cm}$
$\text{\&} \mathit{h}=3 \mathrm{m}.\left[g=\mathrm{10} \mathrm{m} {\mathrm{s}}^{-2}\right]$

A rectangular loop of wire is oriented with the left corner at the origin, one edge along X-axis and the other edge along Y-axis as shown figure. A magnetic field is into the page and has a magnitude that is given by b=$\alpha \text{y}\text{where}\alpha \text{is }$constant. Find the total magnetic force on the loop if it carries current i.

An arc of a circular loop of radius $R$ is kept in the horizontal plane and a
constant magnetic field $B$ is applied in the vertical direction as shown in
the figure. If the arc carries current $I$ then find the force on the arc.

Electric charge $q$ is uniformly distributed over a rod of length $l$. The rod is placed parallel to a long wire carrying a current $i$. The separation between the rod and the wire is $a$. Find the force needed to move the rod along its length with a uniform velocity $v$.

Figure shows a rectangular current-carrying loop placed $2 cm$ away from a long, straight, current-carrying conductor. What is the magnitude of the net force acting on the loop in ${10}^{-4}N$.

A straight wire AB of mass $40 \mathrm{g}$ and length $50 \mathrm{cm}$ is suspended by a pair of flexible leads in uniform magnetic field of magnitude $0.40 \mathrm{T}$ as shown in the figure. The magnitude of the current required in the wire to remove the tension in the supporting leads is _____ $\mathrm{A}$. (Take $\left.g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$.

The net magnetic force on the loop $ABCD$ due the wire is

A uniform rigid ring of radius $r$ and unknown mass is placed on a nonconducting frictionless horizontal tabletop, where exists a uniform horizontal magnetic field of induction $B$ as shown in the figure. A current $I$ that is double of the minimum current required to flip over the ring is made to circulate in the coil. Find force of normal reaction from the tabletop on the ring immediately after the current is switched on.

A rigid metal frame $PQRS$ carries a steady current of $\mathrm{I}=2 \mathrm{A}$ in all $3$ branches as shown in figure. It is in a uniform steady magnetic field of $4 \mathrm{T}$ perpendicular to the plane of the paper. $PQR$ and $PRS$ form two equilateral triangles of side $0.5 \mathrm{m}$ each. The total Lorentz force on the frame $PQRS$ is

A wire of mass $100 \mathrm{g}$ carrying a current of $2 \mathrm{A}$ towards increasing $x$ is in the form of $y=x^2\left(-2 \mathrm{m}\le \mathrm{x}\le +2 \mathrm{m}\right)$. This wire is placed in a magnetic field $B=-0.02\hat{k}$ Tesla and gravity free region. The acceleration of the wire (in $\mathrm{m} {\mathrm{s}}^{-2}$) is:

The force acts for a current carrying conducting loop when magnetic fields is:

The given figure shows an inductor and resistance fixed on a conducting wire. A movable conducting wire $PQ$ starts moving on the fixed rails from $t=0$ with constant velocity $1 \mathrm{m} {\mathrm{s}}^{-1}$. The work done by the external force on the wire $PQ$ in $2$ seconds is