Electromagnetic waves — UPSC CSE 2008 Physics PYQ

A plane electromagnetic wave is travelling in vacuum along a direction which makes an angle of 45^\circ each with the positive x and z-axes. The electric field at time t is given by the expression \bar{E} = E_0 (2 \cos \omega t \hat{j} - \sin \omega t (\hat{i} - \hat{k})) where \hat{i}, \hat{j} and \hat{k} are unit vectors along the x, y and z directions respectively and E_0 = 100 \text{ v/m}. Find the magnetic field vector \bar{B} at time t and obtain the average power transmitted per unit area by the wave.