2. Electromagnetic Fields and Waves

(a) A charge q is moving at velocity through uniform electric and magnetic fields, E and B. The electric field and magnetic field are per- pendicular to each other and to the velocity of the charge. Write down an expression for the total force on the charge and hence determine an expression for the velocity of the charge for the case where the magnitude of the total force is zero.

(b) Two charges of tq and q lie at (-1,0) and (z,0), respectively. Determine an expression for the electric field a distance y along the y-axis.

(c) Unpolarised light of intensity I passes through a pair of linear polarisers. The axis of the first polariser is at 0 degrees to the vertical. After the second polariser, the intensity of light is zero.

i. Use Malus' law to determine the angle that the axis of the second polariser makes with the vertical.

ii. A further linear polariser is inserted between the original two polarisers. The intensity of light passing through all three polarisers

is now Io/8. Determine the angle of the axis of the new polariser with respect to the vertical.