### Basic Electromagnetic Theory

Question 1

(a) Consider two equal point charges separated by a distance d. If a third test charge is inserted at a point exactly midway between the two charges, what is the amount of net force the third charge would experience?

(b) State what happens when:-
i. Two like charges are brought into close proximity to each other. (2 marks)
ii. Two, unlike charges, are brought into close proximity to each other.

(c) State the units for resistivity and for current density.

(d) If the electric potential at a distance of 5cm from an isolated positive point charge is +100V, determine the magnitude of this charge. Use the given formula.

(e) A rectangular carbon block with its dimension is shown in Figure 1. Given the resistivity of carbon at 20°C is ρ=3.5×10-5Ωm, calculate the resistance measured between the two square ends. Use the given formula.

(f) A resistor has a resistance of 30Ω is connected across a battery of emf 8V. Determine:-
i. The current.
ii. The terminal voltage of the battery.
iii. The power delivered by the emf.
iv. The power delivered to the external resistance.

Question 2

(a) A circular coil of radius 1cm has 200 turns. It is removed from a magnetic field of 2T at a time of 0.1s. The field direction is normal to the plane of the coil. i. What is the magnitude of the average voltage induced in the coil?
ii. If the coil is removed more slowly in a time of 1s, what is the magnitude of the voltage induced now?

(b) A conductor located at x = 0.5 m, y = 0, and 0 < z < 2.0 m carries a current of 6.0 A in the direction along the length of the conductor T. Find the torque about the z axis.

(c) The equation for the induced field can be written as, where is the induced field, is the velocity, and is the magnetic field. State the two conditions needed for the field to be induced.

(d) Explain briefly what Maxwell’s equations are used for.

(e) Give four applications of electromagnetic fields.

(f) Maxwell’s equation for Gauss’ law for electric fields is given by. Light is a form of electromagnetic wave and it also consists of photon particles, where they are no free charges.