(a) What is a magnetic field?

(b) With the aid of a labelled diagram describe an experiment to show that a magnetic field exists around a straight wire carrying current.

(c) A 40 \(\mu\)F capacitor in series with a 40 Q resistor is connected to a 100 V, 50 Hz a.c. supply.

(i) Draw a circuit diagram of the arrangement

(ii) Calculate the: I. impedance in the circuit; II. current in the circuit III. potential difference across the capacitor.

(a)(i) State Einstein's equation of photoelectric effect

(ii) What conservation principle does the equation represent?

(b) List three applications of photocells

(c) A photo emissive surface has a threshold frequency of 4.02 x 10\(^{14}\)Hz. If the surface is illuminated by light of frequency 5.0 x 10\(^{15}\)Hz, calculate the:

(i) threshold wavelength;

(ii) work function;

(iii) kinetic energy of the emitted photoelectrons. [ c = 3.0 x 10\(^{8}\) ms\(^{-1}\), h = 6.63 x 10\(^{-34}\) Js]

You are provided with a uniform meter rule, a knife edge, masses and other necessary apparatus.

1. Suspend the metre rule horizontally on the knife edge. Read and record the point of balance G of the métre rule. Keep the knife edge at this point throughout the experiment.
2. Using the thread provided, suspend the object labelled W at the 15cm mark of the metre rule.
3. Suspend a mass M= 20g on the other side of G. Adjust the position of the mass until the metre rule balances horizontally again.
4. Read and record the position Y of the mass M on the metre rule.
5. Determine and record the distance L between the mass and G. Also determine and record the distance D between W and G.
6. Repeat the procedure for four other values of M = 30, 40, 50 and 60 g. In each casse ensure that W is kept Constant at the 15 cm mark and the knife edge at G.
7. Evaluate L\(^{-1}\) in each case. Tabulate your readings.
8. Plot a graph of M on the vertical axis against L\(^{-1}\) on the horizontal axis.
9. Determine the slope S, of the graph.
10. Evaluate \(\frac{4}{D}\)

State two precautions taken to obtain accurate results.
(b)i. State the principle of moments.

ii. Define centre of gravity

Using the above diagram as a guide, carry out the following instructions.

1. Fix a metre rule on the bench with its graduated side facing up.
2. Place the illuminated object at the 0cm end and the screen at the 100cm end of the rule such that the distance d between the illuminated object and screen is 100cm.
3. Record the distance d. Also, evaluate and record d\(^{2}\).
4. Place and move the Converging lens between the illuminated object and the Screen until a sharp diminished image of the object is formed on the screen.
5. Read and record the position Ih of the lens.
6. Now move the lens towards the object until another sharp image of the object is formed on the Screen.
7. Read and record the new position l\(_{2}\) of the lens.
8. Evaluate and record L= (l\(_{1}\) - I\(_{2}\)), also evaluate L\(^{2}\) and D = d\(^{2}\) - L\(^{2}\).
9. Repeat the procedure for four values of d= 85, 75, 65 and 55cm. Tabulate your readings.
10. Plot a graph or Don the vertical axis against d on the horizontal axis.
11. Determine the slope, s, of the graph.
12. Evaluate k = \(\frac{s}{4}\).
13. State two precautions taken to obtain accurate results.

(b)i. Explain the statement the focal length of a converging lens is 15cm.

ii. Distinguish between a real image and a virtual image.

You are provided with two resistance wires labeled and B, a1\(\Omega\) standard resistor Rx, and other necessary apparatus.

1. Connect R\(_{x}\) in the left hand gap of the metre bridge, a length L= 100cm of wire A in the right hand gap, and the other apparatus as shown in the diagram above.
2. Determine and record the balance point P on the bridge wire NQ.
3. Measure and record l\(_{x}\) = NP and l\(_{y}\) = PQ.
4. Evaluate R\(_{1}\) = \(\frac{I_{y}}{L_{x}}\) = R\(_{x}\)
5. Repeat the procedure for four other values of L= 95, 85, 75 and 65cm. In each case, determine and record the balance point P and the length l\(_{x}\) and l\(_{y}\). Also, evaluate R\(_{1}\).
6. Repeat the experiment with the second wire B. Obtain the balance points P and the values of and l\(_{x}\) and l\(_{y}\).
7. Evaluate R\(_{1}\) = \(\frac{I_{y}}{L_{x}}\) = R\(_{x}\) in each case. Tabulate your readings.
8. Plot a graph of R\(_{2}\) on the vertical axis against R\(_{1}\) on the horizontal axis.
9. Determine the slope, s, of the graph.
10. Evaluate k = \(\sqrt s \).
11. State two precautions taken to obtain accurate results.

(b)i. State two advantages of using a potentiometer over a voltmeter for measuring the potential difference.

ii. Define the internal resistance of a cell.