First-year courses · Sciences

Physics II: electricity and magnetism

Coulomb's law, electric fields, Gauss's law, potential, capacitors, DC circuits, Kirchhoff's rules, magnetic forces and induction, with SI unit examples.

44 cards6 topicsAbout 20 minutes a roundTypical first-year physics, second term: electricity, circuits and magnetism

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About this deck

The second term of first-year physics usually switches from mechanics to electricity and magnetism. This deck covers electric charge and Coulomb's law, electric fields and field lines, flux and Gauss's law, electric potential and potential energy, capacitors and dielectrics, current, resistance and Ohm's law, power, series and parallel combinations, Kirchhoff's rules, RC circuits, magnetic forces on charges and wires, fields from currents, and Faraday's and Lenz's laws of induction. Constants used: k = 8.99 x 10^9 N m^2/C^2, epsilon0 = 8.85 x 10^(-12) C^2/(N m^2), mu0 = 4 pi x 10^(-7) T m/A, e = 1.602 x 10^(-19) C.

You will need vectors, forces and energy from the mechanics term, plus scientific notation and metric prefixes (micro is 10^(-6), nano is 10^(-9), milli is 10^(-3)). Prefix slips are the single largest source of wrong numbers in this course.

Many quantities here sound alike (potential versus potential energy, field versus force, flux versus field), so when a card comes up, state the quantity's unit before flipping; if you know the unit you usually know the concept. For circuit and induction cards, sketch the situation and mark directions. Shuffle across tags weekly, because problems routinely link topics, such as a capacitor charging through a resistor.

Common mistakes: adding resistors in parallel as if they were in series (and capacitors the other way around, since their rules are reversed); forgetting that a field is a vector and adding magnitudes from charges that point in different directions; and getting the sign in Lenz's law wrong. The induced current opposes the change in flux, not the flux itself.

Before you start: First-term mechanics (forces, energy, vectors) and comfort with scientific notation; basic calculus is helpful.

All 44 cards

Cover the definitions with a sheet of paper and test yourself, or use the study modes above.

Charge and Coulomb's law

Electric charge: A property of matter, positive or negative, measured in coulombs (C). It is conserved and comes in whole multiples of e = 1.602 x 10^(-19) C.Example: An object with 1.0 C of excess negative charge has about 6.24 x 10^18 extra electrons.
Conductor versus insulator: A material in which charges move freely (metals) versus one in which charges stay roughly where they are placed (glass, plastic, rubber).Example: Charge placed on a metal sphere spreads over its outer surface; on a plastic rod it stays put.
Charging by induction: Charging an object without touching it: bring a charged object near, ground the far side so charge flows, then remove the ground before the charged object.Example: A negative rod near a grounded sphere pushes electrons to ground, leaving the sphere positive.
Coulomb's law: Two point charges exert forces of size F = k|q1 q2|/r^2 on each other, repulsive for like charges and attractive for opposite ones.Example: Two 1.0 microC charges 0.10 m apart: F = 8.99 x 10^9 (10^(-12))/0.01 = 0.899 N.
Superposition principle: The total electric force (or field) from several charges is the vector sum of the contributions from each charge acting alone.Example: Two equal charges at equal distances on opposite sides of a point give zero total field there.

Electric fields and Gauss's law

Electric field: Force per unit positive test charge, E = F/q, in N/C (or V/m). For a point charge its size is kq/r^2, pointing away from positive charges.Example: 2.0 nC at 0.30 m: E = 8.99 x 10^9 (2 x 10^(-9))/0.09 = 200 N/C.
Electric field lines: Curves drawn tangent to the field direction, starting on positive and ending on negative charge; closer spacing means a stronger field. They never cross.Example: Between parallel plates the lines are evenly spaced straight lines: a uniform field.
Electric dipole: A pair of equal and opposite charges separated by a small distance; its dipole moment p = qd points from the negative to the positive charge.Example: A water molecule acts like one, which is why it lines up in an external field.
Electric flux: A measure of how much field passes through a surface: for a uniform field, flux = EA cos(theta), with theta measured from the surface's normal. Unit N m^2/C.Example: E = 500 N/C through 0.02 m^2 at normal incidence: flux = 10 N m^2/C.
Gauss's law: The total electric flux out of any closed surface equals the enclosed charge divided by epsilon0.Example: A closed surface around 1.0 nC has flux 10^(-9)/8.85 x 10^(-12) = 113 N m^2/C, whatever its shape.
Fields from symmetric charge distributions: Gauss's law gives: zero field inside a conductor in equilibrium; sigma/(2 epsilon0) near a large charged sheet; kQ/r^2 outside a charged sphere.Example: Outside a uniformly charged sphere, the field is the same as if all charge sat at its centre.

Potential and capacitors

Electric potential energy: Energy stored in a configuration of charges; for two point charges U = k q1 q2/r (zero at infinite separation).Example: Like charges have positive U, so they release energy as they fly apart.
Electric potential: Potential energy per unit charge, V = U/q, in volts (1 V = 1 J/C). For a point charge, V = kq/r.Example: 2.0 nC at 0.30 m: V = 8.99 x 10^9 (2 x 10^(-9))/0.3 = 59.9 V.
Potential difference and work: Moving charge q through a potential difference delta V changes its potential energy by q delta V.Example: An electron accelerated through 1 V gains 1 electron volt, 1.602 x 10^(-19) J, of kinetic energy.
Field from potential: The field points toward decreasing potential: E = -dV/dx; in a uniform field E = delta V/d.Example: 12 V across plates 3.0 mm apart: E = 12/0.003 = 4000 V/m.
Equipotential surface: A surface on which every point has the same potential; it is always perpendicular to field lines, and moving a charge along it takes no work.Example: Around a point charge these are concentric spheres.
Capacitance: Stored charge per volt for a pair of conductors, C = Q/V, measured in farads (F).Example: A 10 microF capacitor at 12 V holds Q = 120 microC.
Parallel-plate capacitor: C = epsilon0 A/d for plates of area A separated by distance d in vacuum (or air, approximately).Example: A = 0.010 m^2, d = 1.0 mm: C = 8.85 x 10^(-11) F (88.5 pF).
Energy stored in a capacitor: U = (1/2)CV^2 = Q^2/(2C) = (1/2)QV.Example: 10 microF at 12 V: U = 0.5(10^(-5))(144) = 7.2 x 10^(-4) J.
Capacitors in series and parallel: In parallel, capacitances add; in series, reciprocals add: 1/C = 1/C1 + 1/C2 + ...Example: 2 microF and 3 microF: parallel 5 microF, series 1.2 microF.
Dielectric: An insulating material placed between capacitor plates; it multiplies the capacitance by a constant kappa (greater than 1) that depends on the material.Example: Filling an 88.5 pF capacitor with material of kappa = 3 gives 266 pF.

Current and DC circuits

Electric current: The rate at which charge passes a point, I = dQ/dt, in amperes (1 A = 1 C/s). Conventional direction is the direction positive charge would move.Example: 3.0 C passing in 2.0 s is a current of 1.5 A.
Ohm's law: For an ohmic conductor, the voltage across it is proportional to the current through it: V = IR, with R in ohms.Example: 9.0 V across a 3.0 ohm resistor drives 3.0 A.
Resistivity: A material property rho such that a uniform wire has resistance R = rho L/A (length L, cross-sectional area A); unit ohm m.Example: Copper, rho = 1.68 x 10^(-8) ohm m, 10 m long, 1.0 mm^2 area: R = 0.168 ohm.
Electric power in circuits: Rate of energy transfer: P = IV = I^2 R = V^2/R, in watts.Example: A 60 W lamp on 120 V draws 0.5 A and has R = 240 ohm.
Resistors in series: Resistances along a single path add, R_eq = R1 + R2 + ...; the same current flows through each.Example: 2, 4 and 6 ohm in series: 12 ohm.
Resistors in parallel: Reciprocals add, 1/R_eq = 1/R1 + 1/R2 + ...; each branch has the same voltage, and R_eq is less than the smallest branch.Example: 6 ohm and 3 ohm in parallel: 1/R = 1/6 + 2/6, so R = 2 ohm.
EMF and internal resistance: A real battery acts like an ideal source of emf in series with a small internal resistance r, so its terminal voltage is emf - Ir.Example: 12 V battery, r = 0.5 ohm, I = 2 A: terminal voltage 11 V.
Kirchhoff's junction rule: The total current flowing into a junction equals the total current flowing out (conservation of charge).Example: 3 A and 2 A enter a node; 5 A must leave.
Kirchhoff's loop rule: Around any closed loop, the sum of potential changes is zero (conservation of energy): rises across sources equal drops across resistors.Example: 12 V battery with 4 ohm and 2 ohm in series: 12 - 4I - 2I = 0, so I = 2 A.
RC time constant: For a resistor and capacitor in series, tau = RC sets the charging speed; while charging, q(t) = Q(1 - e^(-t/RC)).Example: R = 10 kilohm, C = 100 microF: tau = 1.0 s; after 1 s the capacitor is about 63% charged.
Connecting meters: An ammeter goes in series with the element (ideally zero resistance); a voltmeter goes in parallel across it (ideally infinite resistance).Example: To measure a bulb's current, break the circuit and insert the ammeter in line with the bulb.

Magnetism

Magnetic force on a moving charge: F = q v x B, with size |q|vB sin(theta); it is perpendicular to both v and B, so it changes direction but never speed. B is in teslas (T).Example: Proton at 1.0 x 10^6 m/s perpendicular to 0.50 T: F = 8.0 x 10^(-14) N.
Right-hand rule for v x B: Point fingers along v, curl them toward B; the thumb gives the force direction on a positive charge (reverse it for a negative charge).Example: v east, B north: force on a positive charge points up.
Radius of circular motion in a magnetic field: A charge moving perpendicular to uniform B travels in a circle of radius r = mv/(|q|B).Example: Proton (1.67 x 10^(-27) kg) at 10^6 m/s in 0.50 T: r = 0.021 m.
Force on a current-carrying wire: F = I L x B, with size ILB sin(theta).Example: 2.0 A in 0.50 m of wire perpendicular to 0.30 T: F = 0.30 N.
Field of a long straight wire: B = mu0 I/(2 pi r), circling the wire; direction by the right-hand grip rule (thumb along current).Example: 10 A at 5.0 cm: B = 4.0 x 10^(-5) T, close to Earth's field.
Ampere's law: The line integral of B around a closed loop equals mu0 times the current passing through the loop; useful for highly symmetric currents.Example: It gives the straight-wire field directly: B(2 pi r) = mu0 I.
Solenoid field: Inside a long solenoid, B = mu0 n I, uniform and along the axis, where n is turns per metre.Example: n = 1000 turns/m, I = 2.0 A: B = 2.5 x 10^(-3) T.
Force between parallel currents: Two parallel wires carrying current in the same direction attract; in opposite directions they repel.Example: The force per metre is mu0 I1 I2/(2 pi d), which is how the ampere was historically defined.

Induction

Magnetic flux: Phi_B = BA cos(theta) for a uniform field through a flat area, with theta measured from the normal; unit weber (Wb = T m^2).Example: 0.20 T through 0.050 m^2 face-on: 0.010 Wb.
Faraday's law: A changing magnetic flux through a coil induces an emf: emf = -N d(Phi_B)/dt for N turns.Example: 50 turns, flux changes by 0.010 Wb in 0.10 s: emf = 50(0.1) = 5.0 V.
Lenz's law: The induced current flows in the direction that creates a magnetic field opposing the change in flux that caused it.Example: Push a north pole into a loop: the loop's induced current makes a north face toward the magnet, pushing back.
Motional emf: A conductor of length L moving with speed v perpendicular to a field B has emf = BLv between its ends.Example: 0.20 m rod at 3.0 m/s in 0.50 T: emf = 0.30 V.