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

must reside on its surface.

A uniform plane wave of 100 kHz travelling in free space strikes a large block of a material having

ε = 4 ε₀ , µ = 9µ₀ and σ = 0 normal to the surface. If the incident

magnetic field vector is given by

B = 10^-6 cos (ωt − βy) zˆ tesla

write the complete expressions for the incident, reflected, and transmitted field vectors.

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.

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

A long, straight wire of radius 5.0 mm carries a current of 20A. i) Calculate the magnetic field at the surface of the wire, and ii) calculate the perpendicular distance, from the axis of the wire, at which the magnitude of magnetic field will be half of

its value at the wire surface.

The mass density of copper is 8.95×10³ kg m⁻³. If one charge carrier is contributed by each copper atom, calculate the number density of charge carriers in copper. If

5A current is flowing in a copper wire of cross-sectional area 4×10⁻⁶ m², calculate

the drift velocity of electrons.

Two concentric thin metallic spheres having radii 30 cm and 20 cm carry 10 µC and

5 µC, charges respectively. Calculate the electric potential at a distance of 25 cm

from the centre of the spheres.