Electricity and Magnetism
Electricity and Magnetism: Charge, Circuits, and Fields
This domain combines electrostatics, circuits, and magnetism. Coulomb's law describes the force between point charges: it grows with the product of the charges and falls off with the square of the distance. Electric field strength is force per unit charge, and field lines point from positive to negative charge.
For circuits, Ohm's law relates voltage, current, and resistance. In series circuits, current is the same everywhere and voltages add; equivalent resistance is the sum. In parallel circuits, voltage is the same across each branch and currents add; equivalent resistance is less than the smallest branch resistance. Power dissipated by a resistor can be computed as VI, I²R, or V²/R.
Magnetic effects arise from moving charges and currents. A current-carrying wire in a magnetic field experiences a force perpendicular to both the current and the field (use a right-hand rule). A changing magnetic flux through a loop induces a current-Faraday's law-and the induced current opposes the change that produced it (Lenz's law).
Worked example: Two 6 Ω resistors in parallel across a 12 V source. Each branch carries I = V/R = 2 A, so total current is 4 A and equivalent resistance is 12/4 = 3 Ω. Check: parallel equivalent (3 Ω) is less than either branch (6 Ω), as required.
Traps: adding parallel resistances directly like series; assuming current is "used up" around a series loop; forgetting that magnetic force is zero when the charge moves parallel to the field; and misapplying the direction rules. Always confirm units and that your equivalent resistance obeys the series/parallel sanity checks.