[UPSC CSE 2008] Electromagnetic Theory (Q387, 15M)

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.