Two long, straight, parallel wires A and B, separated by a distance of 30 cm, carry currents I_A = 10A and I_B = 30A. The currents in both the wires flow in the same direction. Calculate the net magnetic field at the midpoint of the line joining the two

wires and perpendicular to them.

Calculate the ratio of the electrostatic force and the gravitational force exerted by protons on each other.

Show that, if there are any unbalanced, static charges on an isolated conductor, they

must reside on its surface.

The line density of charge in a wire is 0.2 Cm⁻¹. If this wire is symmetrically enclosed, along its length, by a cylindrical surface of radius 1 m and length 1.5 m, calculate i) the electric flux through the cylindrical surface, and ii) the electric field

at the curved surface of the cylinder.

Explain the terms polarisation surface charges and molecular polarisability for a

dielectric material.

The radius of the wire in a coaxial cable is 0.65 mm and the inner radius of the coaxial conducting cylinder is 1.45 mm. Assuming that there is vacuum between the

wire and the cylinder, calculate the capacitance of a 1.5 m length of the cable.

Using Maxwell’s equations in free space, derive the wave equation for the

electric field vector. Obtain the conditions under which the following time varying electric and magnetic fields satisfy Maxwell’s equations in vacuum with no source charges or currents:

E = kˆ E0 sin ( y − vt)

B = ˆi B0 sin ( y − vt)

where E₀ and B₀ are constant.