The magnetic field vector of an electromagnetic wave is given by B = B 0 i ^ + j ^ 2 cos k z - ω t where i ^ , j ^ represents unit vector along x and y -axis respectively. At t = 0 s , two electric charges q 1 of 4 π coulomb and q 2 of 2 π coulomb located at 0 , 0 , π k and 0 , 0 , 3 π k , respectively, have the same velocity of 0 . 5 c i ^ , (where c is the velocity of light ). The ratio of

Step-by-step solution

At t = 0 B at 0 ,   0 ,   π k = B 0 i ^ + j ^ 2 cos π B at 0 ,   0 ,   3 π k = B 0 i ^ + j ^ 2 cos 3 π Force on charged particle q 1 F 1 = q 1 V → 1 × B → 1 = 4 π 0 . 5 c i ^ × - B 0 i ^ + j ^ 2 = 4 π B 0 c 2 2 - k ^ Force on charged particle q 2 F 2 = q 2 V → 2 × B → 2 = 2 π 0 . 5 c i ^ × - B 0 i ^ + j ^ 2 = 2 π B 0 c 2 2 - k ^ ⇒ F 1 F 2 = 2