Moving Charges and Magnetism

Moving Charges and Magnetism shows that electricity and magnetism are linked: moving charges and currents produce magnetic fields, and magnetic fields exert forces on moving charges. In this chapter you will start with Oersted's observation that a current deflects a compass needle, and learn the Lorentz force, F = q(E + v x B). You will study the motion of a charged particle in a uniform magnetic field, which is circular or helical, and the idea of a velocity selector using crossed electric and magnetic fields. You will use the Biot-Savart law to find the magnetic field at the centre and on the axis of a circular current loop, and Ampere's circuital law to find the field of a long straight wire and a long solenoid. The chapter explains the force between two parallel currents and the definition of the ampere, the torque on a current loop in a magnetic field, and the current loop as a magnetic dipole. Finally, you will study the moving coil galvanometer and its conversion into an ammeter and a voltmeter.

Detailed Worksheet: Moving Charges and Magnetism Section A - Definitions (10 marks) 1. Write the expression for the Lorentz force on a charge q moving with velocity v in electric field E and magnetic field B. (2 marks) 2. State the Biot-Savart law in vector form. (2 marks) 3. State Ampere's circuital law. (2 marks) 4. Define one ampere in terms of the force between two parallel conductors. (2 marks) 5. Define current sensitivity and voltage sensitivity of a moving coil galvanometer. (2 marks) Section B - Calculations and Applications (15 marks) 6. A circular coil of 100 turns and radius 10 cm carries a current of 1 A. Find the magnetic field at its centre (mu0 = 4 pi x 10^-7 T m/A). (3 marks) 7. An electron moving with speed 4.8 x 10^6 m/s enters a magnetic field of 6.5 x 10^-4 T perpendicular to its velocity. Find the radius of its circular path and its frequency of revolution (m = 9.1 x 10^-31 kg, e = 1.6 x 10^-19 C). (3 marks) 8. A long straight wire carries a current of 35 A. Find the magnetic field at a point 20 cm from the wire. (3 marks) 9. A solenoid of length 0.5 m has 500 turns and carries a current of 5 A. Find the magnetic field inside it. (3 marks) 10. A galvanometer of resistance 12 ohm shows full scale deflection for 3 mA. How will you convert it into (i) an ammeter of range 0 to 6 A and (ii) a voltmeter of range 0 to 18 V? (3 marks) Section C - Diagrams (10 marks) 11. Draw a labelled diagram of a moving coil galvanometer showing the coil, radial magnetic field, soft iron core, spring and pointer. Explain why a radial field is used. (4 marks) 12. Draw the magnetic field lines around a long straight current-carrying wire and inside and outside a long solenoid. (3 marks) 13. Draw the helical path of a charged particle whose velocity makes an angle with a uniform magnetic field, marking the pitch and radius. (3 marks) Section D - Analysis and Higher-order Thinking (15 marks) 14. Two long straight parallel wires 4 cm apart carry currents of 8 A and 5 A in opposite directions. Find the force on a 10 cm length of the 5 A wire and state whether it is attractive or repulsive. Derive the formula used. (5 marks) 15. A square coil of side 10 cm with 20 turns carries a current of 12 A. It is suspended vertically with the normal to its plane at 30 degrees to a uniform horizontal field of 0.80 T. Find the torque on the coil. Explain the position of stable equilibrium. (5 marks) 16. Using the Biot-Savart law, derive the magnetic field on the axis of a circular current loop. Show that at the centre it reduces to mu0 I/(2R) and at large distances it behaves like a magnetic dipole. (5 marks) Instructions: Time allowed 2 hours. Attempt all sections. Use mu0 = 4 pi x 10^-7 T m/A and show directions using the right hand rule.