(a) Elecromotive force is the energy needed to take a unit positive charge round a circuit in which a cell is connected. Or The energy per unit charge transformed in the cell. Or e.m.f is the p.d across the terminals of the cell or battery or generator in an open circuit. (b)(i) The principle of operation of a potentiometer is based on the fact that the p.d across the wire is directly proportional to the length of the wire.V \(\alpha\) L where V = p.d across the wire. L = length of the wire. (ii) Advantages of potentiometer over voltmeter in measuring p.d are: (1) It is more sensitive. (2) It is more accurate. (3) It eliminates error due to internal resistance of the cell. (c)(i) Labelled sketch of a Gold leaf electroscope: (ii) Uses of Gold leaf electroscope are: (1) To detetct the nature of electrostatic charge. (2) To detect electrostatic charge. (3) To determine the magnitude of the induced charges. (d)(i) The mode of action of magnetic relay relies on the principle of electromagnetic induction. A small current passing through one circuit controls another circuit containing devices which require larger current. (ii) Factors affecting the magnitude of induced e.m.f in a coil are: (1) the number of turns in the coil. (2) the magnetic field strength. (3) the cross-sectional area of the coil. (4) the speed of rotation of the coil. (iii) F = IBLsin\(\theta\) force per unit length \(\frac{F}{L}\) = IBsin\(\theta\) = 5 x 2.0 x 10\(^{-3}\) x sin30 = 5.0 x 10\(^{-3}\)Nm\(^{-1}\)