Where necessary use the following constants Permeability of free space() Permittivity of free space(E.) Velocity of light (c) Mass of electron (m.) Mass of proton (mp) Charge on an electron Charge on a proton Question One a. Write the Laplace an Poison equations (2 marks) b. What are the four Maxwell equations in differential form and which law does each represent? (4 marks) c. A single-loop circuit contains two resistors and two batteries as shown in Figure 1 below. (Neglect the internal resistances of the batteries.) Find the current in the circuit. (4 marks) a d 8 = 6.0 V + R = 10 4x x 107 henry/meter 8.85x10CNm 3.0 108 ms 9.11 10-1 kg 1.67 1027 kg -1.610C 1.610 C I R8.0 23 + 8= 12 V C Figure 1 d. A 200 resistor is connected in series with a 5.0-microF capacitor. The voltage across the resistor is v=(1.20 V)cos(2500 rads/sec)t. i Write an expression for the circuit current. (2 marks) ii Determine the capacitive reactance of the capacitor. iii Derive an expression for the voltage across the capacitor. (2 marks) (2 marks) e. The maximum working flux density of a lifting electromagnet is 1.6 T and the effective area of a pole face is circular in cross-section. If the total magnetic flux produced is 353mWb, determine the radius of the pole face. (3 marks) f. Electronic gadgets today use transistors in place of vacuum tubes which were popular in the past. Highlight any three advantages of transistors over vacuum tubes. (3 marks) g. Consider a uniform electric field E oriented in the x direction in empty space. A cube of edge length, 1, is placed in the field, oriented as shown in Figure 2 below. Find the net electric flux through the surface of the cube. (4 marks) d dAs dA Figure 2 h. Starting from Vcc= IcRc + Vce, where the symbols have their usual meanings, obtain the equation for a transistor loadline of a CE amplifier and show that it is the equation of a straight line. (4 marks)