Embibe Experts Solutions for Chapter: Magnetic Effect of Current and Magnetism, Exercise 1: Exercise 1

In a certain region of space, electric field $\overrightarrow{E}$ and magnetic field $\overrightarrow{B}$ are perpendicular to each other and an electron enters in region perpendicular to the direction of $\overrightarrow{B}$ and $\overrightarrow{E}$ both and moves undeflected. Then velocity of electron is

Which particles will have minimum frequency of revolution when projected with the same velocity perpendicular to a magnetic field?

A proton of energy $8 \mathrm{eV}$ is moving in a circular path in uniform magnetic field. The energy of an $\alpha$ -particle moving in the same magnetic field and along the same path will be

A current carrying square loop is placed near a straight infinitely long current carrying wire as shown in figure. The torque acting on the loop is

Two parallel conducting wires of equal lengths placed distance $d$ apart carry currents $I_1$ and $I_2$ respectively in opposite directions. The resultant magnetic field at the midpoint of both the wires is (${\mu }_{\mathrm{o}}=$ permeability of free space.)

A very long straight wire of radius $r$ carries current $I$. Intensity of magnetic field $B$ at a point lying at a perpendicular distance $a$ from the axis is $\propto$ _____ $(\text{where} a<r)$.

A bar magnet of magnetic moment $5 \mathrm{A} {\mathrm{m}}^2$ is placed in a uniform magnetic induction $3\times {10}^{-5} \mathrm{T}.$ If each pole of a magnet experiences a force of $2.5\times {10}^{-4} \mathrm{N}$ then the magnetic length of the magnet is

A magnetic dipole of moment $\overrightarrow{m}$ is placed in the magnetic field $\overrightarrow{B}$. It is free to rotate about an axis about which its moment of inertia is $I$. It is displaced by a small angle ${\theta }_0\left({\theta }_0<<1\right)$ at time $t=0 \mathrm{s}$ and released. The dipole undergoes simple harmonic motion with angular frequency $\omega$. Its potential energy at time $t$ is : (Assume $\sin \left(\alpha \right)\approx \alpha , \cos \left(\alpha \right)\approx 1-\frac{{\alpha }^2}{2}$ if $\alpha <<1$)