Electric Charges and Fields

Electric Charges and Fields is the first chapter of electrostatics, the study of charges at rest. In this chapter you will learn about the two kinds of charge, charging by friction, conduction and induction, and the basic properties of charge: additivity, conservation and quantisation, q = ne. You will use Coulomb's law to find the force between point charges, and the principle of superposition to find the net force on a charge due to several others. You will then define the electric field, calculate the field due to a point charge and a system of charges, and draw electric field lines with their properties. You will study the electric dipole, the field on its axial and equatorial lines, and the torque on a dipole in a uniform field. The chapter introduces electric flux and Gauss's law, which states that the flux through a closed surface equals the enclosed charge divided by epsilon0. You will apply Gauss's law to find the field due to an infinitely long straight wire, an infinite plane sheet and a thin spherical shell.

Detailed Worksheet: Electric Charges and Fields Section A - Definitions (10 marks) 1. State the quantisation and conservation of electric charge. (2 marks) 2. State Coulomb's law in vector form. (2 marks) 3. Define electric field at a point. Write its SI unit. (2 marks) 4. Define electric dipole moment. What is its direction? (2 marks) 5. State Gauss's law in electrostatics. (2 marks) Section B - Calculations and Applications (15 marks) 6. Two point charges of +2 microC and -3 microC are placed 30 cm apart in air. Find the magnitude and nature of the force between them (k = 9 x 10^9 N m^2 C^-2). (3 marks) 7. A plastic comb rubbed with dry hair acquires a charge of -3.2 x 10^-9 C. How many electrons has it gained? What is the change in its mass (m of electron = 9.1 x 10^-31 kg)? (3 marks) 8. Charges of +10 microC and -10 microC are placed 20 cm apart. Find the electric field at the midpoint of the line joining them and state its direction. (3 marks) 9. An electric dipole of moment 4 x 10^-9 C m is aligned at 30 degrees to a uniform electric field of 5 x 10^4 N/C. Calculate the torque on the dipole. (3 marks) 10. A point charge of 2.0 microC is at the centre of a cube of side 9.0 cm. Find the electric flux through the whole cube and through each face (epsilon0 = 8.854 x 10^-12 C^2 N^-1 m^-2). (3 marks) Section C - Diagrams (10 marks) 11. Draw the electric field lines for (i) a single positive charge, (ii) an electric dipole and (iii) two equal positive charges. State four properties of field lines. (4 marks) 12. Draw a diagram showing an electric dipole in a uniform electric field, marking the forces on the charges and the torque. (3 marks) 13. Draw a graph showing the variation of electric field with distance from the centre of a charged thin spherical shell of radius R, both inside and outside. (3 marks) Section D - Analysis and Higher-order Thinking (15 marks) 14. Using Gauss's law, derive the electric field due to an infinitely long straight wire of uniform linear charge density lambda. Hence find the field at 2 cm from a wire with lambda = 3 x 10^-6 C/m. (5 marks) 15. Two large thin metal plates are parallel and close to each other. On their inner faces, the plates have surface charge densities of opposite signs and magnitude 17.0 x 10^-22 C/m^2. Using Gauss's law, find the electric field (i) outside the plates and (ii) between the plates. (5 marks) 16. A conducting sphere of radius 10 cm has an unknown charge. The electric field 20 cm from its centre is 1.5 x 10^3 N/C directed radially inward. Find the net charge on the sphere and the electric flux through a sphere of radius 20 cm concentric with it. (5 marks) Instructions: Time allowed 2 hours. Attempt all sections. Use k = 9 x 10^9 N m^2 C^-2 and show directions of forces and fields clearly.