Electrostatic Potential and Capacitance

Electrostatic Potential and Capacitance describes electrostatics in terms of energy, which is often simpler than working with forces and fields. In this chapter you will learn that the electrostatic force is conservative, define electrostatic potential and potential difference, and derive the potential due to a point charge, an electric dipole and a system of charges. You will draw equipotential surfaces, relate the electric field to the potential gradient, and find the potential energy of a system of charges and of a dipole in an external field. You will then study conductors and dielectrics in electrostatic fields, including electrostatic shielding, polarisation and the dielectric constant. The second half of the chapter deals with capacitors, devices that store charge and energy. You will derive the capacitance of a parallel plate capacitor with and without a dielectric, combine capacitors in series and parallel, and derive the energy stored in a capacitor, U = (1/2)CV^2, and the energy density of an electric field.

Detailed Worksheet: Electrostatic Potential and Capacitance Section A - Definitions (10 marks) 1. Define electrostatic potential at a point. Write its SI unit. (2 marks) 2. What is an equipotential surface? Why is no work done in moving a charge on it? (2 marks) 3. Write the relation between electric field and potential. What does the negative sign signify? (2 marks) 4. Define capacitance of a capacitor. On what factors does the capacitance of a parallel plate capacitor depend? (2 marks) 5. What is a dielectric? Define dielectric constant. (2 marks) Section B - Calculations and Applications (15 marks) 6. Find the potential at a point 9 cm from a charge of 4 x 10^-7 C. Find the work done in bringing a charge of 2 x 10^-9 C from infinity to this point. (3 marks) 7. Two charges of 5 x 10^-8 C and -3 x 10^-8 C are located 16 cm apart. At what points on the line joining them is the electric potential zero? Take the potential at infinity as zero. (3 marks) 8. A parallel plate capacitor with air between the plates has plate area 6 x 10^-3 m^2 and separation 3 mm. Find its capacitance and the charge on each plate when connected to a 100 V supply (epsilon0 = 8.85 x 10^-12 F/m). (3 marks) 9. Three capacitors, each of 9 pF, are connected in series to a 120 V supply. Find the total capacitance and the potential difference across each. (3 marks) 10. A 12 pF capacitor is connected to a 50 V battery. How much electrostatic energy is stored in it? (3 marks) Section C - Diagrams (10 marks) 11. Draw the equipotential surfaces for (i) a point charge, (ii) a uniform electric field and (iii) an electric dipole, with field lines. (4 marks) 12. Draw a labelled diagram of a parallel plate capacitor with a dielectric slab, showing the polarisation charges and the reduced field inside the dielectric. (3 marks) 13. Draw circuit diagrams of three capacitors in series and in parallel and write the formula for the equivalent capacitance in each case. (3 marks) Section D - Analysis and Higher-order Thinking (15 marks) 14. A 600 pF capacitor is charged by a 200 V supply and then disconnected and connected to another uncharged 600 pF capacitor. Find the common potential, the initial and final energies and the energy lost. Where does this energy go? (5 marks) 15. A parallel plate capacitor is charged by a battery and a dielectric slab of constant K is then inserted to fill the space between the plates. Compare the changes in capacitance, charge, potential difference, electric field and energy when (i) the battery remains connected and (ii) the battery is disconnected before inserting the slab. (5 marks) 16. Three charges of +1 microC, +1 microC and -2 microC are placed at the corners of an equilateral triangle of side 10 cm. Find the potential energy of the system. Explain the meaning of its sign. (5 marks) Instructions: Time allowed 2 hours. Attempt all sections. Use k = 9 x 10^9 N m^2 C^-2 and epsilon0 = 8.85 x 10^-12 F/m. Show units at every step.