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.

If the space between the plates of a capacitor is filled will a dielectric material, does

it affect the value of capacitance? Justify your answer.

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.

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.

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.

State and explain the boundary condition for the displacement vector D at the

boundary separating two dielectric media.

An electron and a proton, moving with equal velocity, enter a region of uniform, perpendicular magnetic field. Calculate the ratio of the radii of their circular paths in

the field.