AP Physics C: E&M review
AP Physics C: Electricity and Magnetism is often called the hardest AP physics course. Clear structure and steady practice make it manageable.
On this page
The units
- Electric Charges, Fields, and Gauss's Law
- Electric Potential
- Conductors and Capacitors
- Electric Circuits, including RC circuits
- Magnetic Fields and Electromagnetism
- Electromagnetic Induction, including LR and LC circuits
Check the current course and exam description on AP Central for details.
The key laws
- Gauss's law for the electric field of symmetric charge distributions.
- Potential from integrating the field: ΔV = −∫E·dr.
- Biot-Savart and Ampère's law for magnetic fields of currents.
- Faraday's law and Lenz's law for induced emf and its direction.
Skills that earn marks
- Choosing a Gaussian surface or Ampèrian loop that matches the symmetry.
- Setting up integrals with correct limits.
- Solving and sketching exponential behaviour in RC and LR circuits.
- Using right-hand rules confidently.
A review plan
- Make a one-page summary of each law with a sketch.
- Practise one symmetry problem and one circuit problem each day.
- Work through past free-response questions with the scoring guidelines.
Worked examples
Example 1: field of a charged sphere
A conducting sphere of radius R carries charge Q. Find the field inside and outside.
- Inside a conductor in equilibrium, E = 0.
- Outside, a spherical Gaussian surface gives E(4πr²) = Q/ε0, so E = Q/(4πε0r²), as if all the charge were at the centre.
Example 2: potential difference from a field
A uniform field of 500 V/m points in the +x direction. Find V(0.2 m) − V(0).
- ΔV = −∫E dx = −500 × 0.2 = −100 V. Potential falls in the direction of the field.
Example 3: capacitors in series
A 2 µF and a 6 µF capacitor are connected in series to 12 V. Find the charge on each.
- 1/C = 1/2 + 1/6 = 2/3, so C = 1.5 µF.
- Q = CV = 1.5 × 12 = 18 µC on each, because series capacitors carry the same charge.
Example 4: an LR circuit
A 9 V battery is connected to a 3 Ω resistor and a 0.6 H inductor. Find the time constant and the final current.
- τ = L/R = 0.2 s. Final current = 9/3 = 3 A, reached gradually as the inductor's opposition fades.
Practice questions
Try each one before opening the answer.
Q1. Find the magnetic field at the centre of a circular loop of radius R carrying current I.
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Q2. A solenoid has 2000 turns per metre and carries 0.5 A. Find B inside. Use μ0 = 4π × 10−7 T·m/A.
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Q3. Immediately after a switch is closed in an RC charging circuit, how does the uncharged capacitor behave?
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Common mistakes
- Forgetting that E = 0 inside a conductor in electrostatic equilibrium.
- Mixing up series and parallel rules for capacitors, which are the reverse of resistors.
- Getting the direction of induced current wrong. Apply Lenz's law every time.
The key ideas in more depth
Charge, field and potential
The electric field tells you the force per unit charge at a point. The potential tells you the energy per unit charge. They are linked: the field points in the direction in which potential falls fastest, and E = −dV/dr. If you know one, you can find the other by integrating or differentiating. Many free-response questions give you a field and ask for a potential difference, or the other way round.
Why symmetry matters
Gauss's law is always true, but it is only useful when symmetry lets you pull E outside the integral. That happens for three shapes: spheres, long cylinders (wires) and large flat sheets. For each one, choose a Gaussian surface where E is constant in size and either parallel or perpendicular to the surface. Ampère's law works the same way for magnetic fields around long wires, solenoids and toroids.
Circuits that change with time
In RC and LR circuits, currents and voltages change exponentially. The time constant (RC or L/R) sets how fast. Two moments are always worth checking. Immediately after a switch moves, a capacitor acts like a wire (if uncharged) and an inductor acts like a break in the circuit. A long time later, a capacitor acts like a break and an inductor like a wire. These limits let you answer many questions without solving any differential equation.
Induction and Lenz's law
A changing magnetic flux through a loop induces an emf. The induced current always flows so that its own magnetic field opposes the change in flux. Ask: is the flux increasing or decreasing, and in which direction? Then choose the current direction that fights that change.
Exam tips for E&M
- Draw field lines, Gaussian surfaces and current directions on every diagram you are given.
- Keep vector directions in words as well as symbols, for example "toward the wire".
- When asked to "derive", start from a fundamental law, such as Gauss, Ampère or Kirchhoff, not a memorised result.
- Sketch graphs with correct starting values, limits and shapes; these earn marks even without numbers.
More practice
Try each one before opening the answer.
Q1. A large flat sheet has charge per unit area σ. Use Gauss's law to find E near it.
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Q2. A long time after a switch closes in an LR circuit, what is the voltage across an ideal inductor?
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Q3. A bar magnet's north pole is pushed toward a coil. Which pole does the coil's induced field present toward the magnet?
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Frequently asked questions
Is E&M harder than Mechanics?
Many students find it harder because the ideas are less visible. Drawing fields and potentials helps make them concrete.
Which right-hand rule should I use?
Use one rule consistently for the force on a moving charge and one for the field around a current. Practise both until they are automatic.
Key takeaways
- The field and the potential are linked by E = −dV/dr.
- Gauss's law and Ampère's law rely on symmetry.
- Capacitors and inductors make circuits change exponentially.
- Check the limits just after a switch moves and a long time later.
- Lenz's law gives the direction of every induced current.
Quick check
Two 3 µF capacitors are connected in parallel. Find the total capacitance.