A proton, an electron, and a Helium nucleus, have the same energy. They are in circular orbits in a plane due to magnetic field perpendicualr to the plane. Let r_p, r_e and r_He be their respective radii, then

A particle of mass m is moving along a trajectory given by
x = x₀ + a cos$$\omega $$₁t
y = y₀ + b sin$$\omega $$₂t
The torque, acting on the particle about the origin, at t = 0 is :

The electric field of a plane electromagnetic wave is given by
$$\overrightarrow E = {E_0}\widehat i\cos (kz)cos(\omega t)$$
The corresponding magnetic field $$\overrightarrow B $$ is then given by

Two coaxial discs, having moments of inertia I₁ and I₁/2, are rotating with respective angular velocities $$\omega $$₁ and $$\omega $$₁/2 , about their common axis. They are brought in contact with each other and thereafter they rotate with a common angular velocity. If E_f and E_i are the final and initial total energies, then (E_f - E_i) is: