NCERT Solutions for Chapter: Moving Charges and Magnetism, Exercise 2: VSA

Verify that the cyclotron frequency $\omega =e B/m$ has the correct dimensions of $[\mathrm{T}{]}^{-1}$

Show that a force that does no work must be a velocity dependent force.

The magnetic force depends on $\mathrm{v}$ which depends on the Inertial frame of reference. Does then the magnetic force differ from Inertial frame to frame? Is It reasonable that the net acceleration has a different value In different frames of reference?

Describe the motion of a charged particle in a cyclotron if the frequency of the radio frequency (rf) field were doubled.

Two long wires carrying current $I_1$ and $I_2$ are arranged as shown in figure. The one carrying current $I_1$ is along the $x$-axis. The other carrying current $I_2$ is along a line parallel to the $y$-axis given by $x=0$ and $z=d$. Find the force exerted at $O_2$ because of the wire along the $x$-axis.