Chapter 12: Electricity and Magnetism

Electrostatics

Coulomb’s law: with . The electric field is ; for a point charge . Potential and field and potential are related by . Example: two charges of separated by 0.1 m exert a force N.

Capacitors store charge: ; for parallel plates ; energy . In parallel, ; in series, . In an RC circuit the capacitor charges as , with time constant (for and , s).

Current electricity

Current . Ohm’s law: for ohmic conductors. Resistivity: . Power: . Resistors in series add; in parallel (so and in parallel give ).

A real source has e.m.f. and internal resistance ; terminal voltage . Example: V, , load : A, V.

Kirchhoff’s laws: the sum of currents at a junction is zero (charge conservation); the sum of e.m.f.s equals the sum of potential drops around a loop (energy conservation). Applications include the potential divider and the Wheatstone bridge (balanced when ).

Magnetism

A charge moving in a magnetic field experiences ; a current-carrying wire of length experiences (directions by the left-hand rule). A charge moving perpendicular to follows a circle of radius . A long straight wire produces ; a solenoid has , with (approximately).

Electromagnetic induction

Faraday’s law: the induced e.m.f. equals the rate of change of magnetic flux linkage, ; Lenz’s law (the minus sign) says that the induced current opposes the change that produces it. A rod of length moving at speed perpendicular to field has . Self-inductance gives and stored energy . Generators and transformers rely on induction; for an ideal transformer . Example: stepping down 240 V to 12 V with 1200 primary turns needs 60 secondary turns.

Alternating current

For , the r.m.s. value is . In a series LCR circuit, the impedance is with and . Resonance occurs when , at ; for mH and nF, kHz. Rectification (diodes) converts AC to DC.

Common mistakes

Forgetting that the e.m.f. is not equal to the terminal voltage when current flows.

Mixing up field lines of E (start on + and end on −) with those of B (closed loops).

Using peak values in power calculations instead of r.m.s.

Practice questions

Find the equivalent capacitance of and in series. [3 μF]

A proton moves at perpendicular to a 0.1 T field. Find the radius of its path. ( kg) [≈0.209 m]

A resistor of 20 Ω carries an r.m.s. current of 3 A. Find the mean power. [180 W]