Physics 2: Electricity and Magnetism: practice problems and exam questions

Electric charges, forces and fields, DC circuits, capacitors and RC circuits, and alternating current: the second semester of university physics.

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Cram pack (PDF)Formula sheets, method steps and practice problems with full solutions, ready to print.

Topics in this course

  1. Coulomb’s law & electric fieldsforce between two charges · field between two charges · forces at a right anglecalculations
  2. Series & parallel resistors3 resistors · 4 resistors · ladder of 6 resistorscalculations
  3. RC & RL transientsRC charging · RL circuit · capacitor with initial chargecalculations
  4. Magnetic fields & inductionfields of currents and magnetic forces · charged particles, Faraday and Lenz · generators, inductance and particle beamscalculations
  5. AC impedance & phasorsseries RL · series RLC · capacitor voltage and resonancecalculations

Exam tips for Physics 2: Electricity and Magnetism

  • Forces and fields from several charges add as vectors: draw each one before you add.
  • Convert µC to C and cm to m before using Coulomb’s law.
  • A capacitor blocks DC once it is charged; the time constant τ = RC sets how fast that happens.
  • For magnetic forces and induced currents, sketch ⊗ and ⊙ and use the right-hand rule every time: most lost points are wrong directions.

Worked examples

Coulomb’s law & electric fieldsEasy
++4 µC++1 µCr = ?

Point charges of +4 µC and +1 µC exert a force of 20 N on each other. How far apart r are they? Give the answer in cm. Use k = 8.99 × 10⁹ N·m²/C².

q1 = +4 µCq2 = +1 µCF = 20 N

Find r (cm)

Show hints
  1. Rearrange Coulomb’s law for r.
  2. r = √(k·|q₁·q₂|/F).
  3. r² = 0.001798 m².
Show the answer and the step-by-step solution

Coulomb’s law: two point charges attract or repel with F = k·|q₁·q₂|/r², with k = 8.99 × 10⁹ N·m²/C². The field of a point charge is E = k·|q|/r², pointing away from a positive charge and towards a negative one. Forces and fields from several charges add as vectors.

Solve for the distance

r = √(8.99 × 10⁹·4 × 10⁻⁶·1 × 10⁻⁶/20) = 0.0424 m
r = 4.24 cm

Answer

r = 4.24 cm
Series & parallel resistorsMedium
R1​ = 6 ΩIR1​R3​ = 3 Ω+−V1​18 VR2​3 ΩAR4​6 ΩB

Find the current IR1 delivered by the source, which flows through R1.

V1 = 18 VR1 = 6 ΩR2 = 3 ΩR3 = 3 ΩR4 = 6 Ω

Find IR1 (A)

Show hints
  1. Reduce the network step by step. In series, resistances add. Two resistors in parallel combine as R₁R₂/(R₁ + R₂).
  2. R₃ and R₄ carry the same current, so they are in series. That branch is in parallel with R₂, and the result is in series with R₁.
  3. Req = 8.25 Ω.
Show the answer and the step-by-step solution

Series and parallel resistors: in series the same current flows through each resistor and R = R₁ + R₂ + …. In parallel each resistor has the same voltage and 1/R = 1/R₁ + 1/R₂ + …. A ladder network is reduced one pair at a time until a single equivalent resistance remains.

R1​ = 6 ΩR3​ = 3 Ω+−V1​18 VR2​3 ΩAR4​6 ΩB

Combine resistors from the far end

Start at the end farthest from the source and work back towards it. Resistors carrying the same current are in series; resistors across the same two nodes are in parallel.

R3 + R4 = 3 + 6 = 9 Ω
R2 ∥ 9 = 3·9/(3+9) = 2.25 Ω
Req = R1 + 2.25 = 6 + 2.25 = 8.25 Ω

Current from the source

The source sees only Req, so Ohm’s law gives the current it delivers. That current flows through R₁.

IR1 = V1/Req = 18/8.25 = 2.182 A

Answer

IR1 = 2.182 A

How practising works

  • “Practise this course” mixes problems from all its topics, like a real exam.
  • Every problem has new values, so you learn the method instead of an answer.
  • Stuck? Open a small hint first, and the full explanation only when you need it.
  • Mock exams are timed and have no hints, and you get your score and a full review at the end.

Calculators for this course

Series and parallel resistor calculatorVoltage divider calculatorRC time constant calculatorRLC impedance calculatorCoulomb’s law calculatorOhm’s law calculator (voltage, current, resistance and power)Resistor colour code calculator (4, 5 and 6 bands)Capacitor calculator (series, parallel, charge and energy)Magnetic field calculator (wire, loop, solenoid and toroid)

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Practise this course for freePractise this courseTake a mock exam5 free problems every day. No card needed.