Question

The electric field of a plane electromagnetic wave is given by vector E = E₀((i + j)/√2) cos (kz + ωt). At t = 0, a positively charged particle is at the point (x, y, z) = (0,0,(π/k)). If its instantaneous velocity at (t = 0) is v₀k , the force acting on it due to the wave is :

(1) zero

(2) parallel to (i + j)/√2

(3) antiparallel to (i + j)/√2

(4) parallel to k

Answer 1

Answer is (3) antiparallel to (i + j)/√2 

since v0/c << 1

F is antiparallel to (i + j)/√2

Answer 2

Answer is (3) antiparallel to ((i + j)/√2)

Force due to electric field is in direction = (i + j)/√2

because at t = 0, E = ((i + j)/√2)E₀

Force due to magnetic field is in direction q vector(v x B) and vector (v || k)

It is parallel to vector E

net force is antiparallel to (i + j)/√2