The magnetic field of an electromagnetic wave is given by B = B₀ (0.6 i + 0.8 j ) (kz + t) . A point charge q is moving with a velocity v = v₀ k at the origin at t=0 . The instantaneous Lorentz force on the charge at t=0 is :

Step-by-step solution

At the origin ( z=0 ) and at t=0 , the magnetic field is: B = B₀ (0.6 i + 0.8 j ) From the phase argument (kz + t) , the wave is propagating in the -z direction, so k _ prop = - k . The electric field vector E is given by E = c( B k _ prop ) . E = c [B₀ (0.6 i + 0.8 j ) (- k )] E = c B₀ [-0.6( i k ) - 0.8( j k )] E = c B₀ [-0.6(- j ) - 0.8( i )] = c B₀ (-0.8 i + 0.6 j ) The electric force on the charge is: F _e = q E = q c B₀ (-0.8 i + 0.6 j ) The magnetic force on the charge is: F _m = q( v B ) = q [v₀ k B₀ (0.6 i