Embibe Experts Solutions for Chapter: Magnetic Effect of Current, Exercise 3: Exercise-3

A square loop $ABCD$ carrying a current $i$, is placed near and coplanar with a long straight conductor $XY$ carrying a current $I$, the net force on the loop will be

A cylindrical conductor of the radius $R$ is carrying a constant current. The plot of the magnitude of the magnetic field $B$, with the distance $d$ from the centre of the conductor, is correctly represented by the figure:

Proton, Deuteron and alpha particle of 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 relation is correct?

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 ($g=$ gravitational acceleration)

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

$\left(\mathrm{a}\right)$  $\left(\mathrm{b}\right)$ 

$\left(\mathrm{c}\right)$ $\left(\mathrm{d}\right)$ 

If there is a uniform magnetic field of $0.3 \mathrm{T}$ in the positive $z$-direction, in which orientations the loop would be in $\left(\mathrm{i}\right)$ stable equilibrium and $\left(\mathrm{ii}\right)$ unstable equilibrium?

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 $d\left(d\gg a\right)$. If the loop applies a force $F$ on the wire then

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

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