General aim:

This part of the course introduces new concepts: capacitance, inductance, impedance, reactance, self inductance. It introduces new techniques for investigating electric and magnetic fields. The importance of high input and low output impedance of circuit devices is emphasised. The dc and ac response of RC circuits, and when they can be used to integrate or differentiate the applied wave form, is studied.

Objectives

1 On completion of this section, you should be able to:

• Write an account of Faraday's experiments on electromagnetic induction;
• Define magnetic flux;
• State Faraday's law of electromagnetic induction and Lenz's law;
• Find the current induced by a varying magnetic field in a circuit of given dimensions and resistance;
• Calculate the emf induced in a straight wire moving in a magnetic field;
• Calculate the emf induced in a plane coil rotating in a magnetic field;
• Define self-inductance L and explain its relation to the current flowing in a circuit and the resulting magnetic flux linking the circuit;
• Derive an expression for the emf induced when the current varies;
• Relate L to the number of turns in a uniformly wound coil of wire, the relative permeability of the surrounding material and the self inductance of one turn;
• Calculate the self-inductance of a solenoid;
• Derive an expression for the growth of current in a series LR circuit when connected to a battery and the decay when shorted;
• Define and derive an expression for the time constant of an RL circuit;
• Define the mutual inductance between two circuits.

2 On completion of this section, you should be able to:

• Define electric flux through a surface;
• Write down and prove Gauss's law of electrostatics;
• Use Gauss's law to derive the electric field surrounding and within spherically symmetric or cylindrically symmetric charge distributions;
• Use Gauss's law to calculate the electric field due to a plane sheet of charge;
• Show that, on passing through a sheet of charge, the component of electric field parallel to the sheet is unchanged, while;
• The component normal to the sheet has a discontinuity equal to the areal charge density divided by the permittivity of free space;
• Define electric potential;
• Explain what is meant by an equipotential surface;
• Define capacitance;
• Derive expressions for the capacitance of a parallel plate capacitor;
• Define relative permittivity in terms of capacitance;
• Show that the voltage and electric field in a capacitor are reduced if a dielectric is introduced;
• between the plates;
• Analyse an RC circuit.

3 On completion of this section, you should be able to:

• Differentiate between transient and steady-state behaviour;
• Write down and derive expressions for the complex impedance of a resistor, inductor and capacitor;
• Explain how a complex impedance contains information on amplitude and phase change;
• Combine impedances in series and in parallel;
• Calculate the magnitude and phases of currents and voltages in simple LCR networks;
• Describe the free oscillations of a series LCR circuit and identify the quality factor;
• Analyse the forced oscillations of a series LCR circuit and discuss resonance;
• Analyse the forced oscillations of a parallel LCR circuit and discuss its use as a radio tuner;
• State the properties of ideal and real operational amplifiers;
• Define the term virtual earth;
• Explain why RC circuits can be used to integrate or differentiate an applied wave form;
• Design differentiators and integrators using operational amplifiers;
• Identify and solve problems requiring familiarity with the above.