AP Physics C: Electricity and Magnetism Lab InvestigationsCalculus Based Inquiry Across All 5 Units

The required AP Physics C: Electricity and Magnetism lab investigations

1. 1

   Mapping Electric Fields and Equipotential Surfaces

   BI1, BI2

   Students place two conducting electrodes in a shallow conducting solution and use a voltage sensor or multimeter to map points of equal potential, tracing equipotential curves across the tray. Field lines are then drawn perpendicular to the equipotential curves, revealing the spatial structure of the electric field between and around the electrodes. The investigation makes the abstract relationship E equals negative dV/dr concrete and measurable: where equipotential lines are closely spaced, the field is strong. Students connect their mapped field geometry to Gauss's law predictions and the superposition principle, explaining why field lines originate on positive charge and terminate on negative charge. Measurements include potential at a grid of points, spacing between equipotentials, and the direction of the local field vector. Uncertainty analysis covers probe positioning error and contact resistance in the conducting solution.

   On the exam: FRQ subparts ask students to sketch field lines consistent with a given charge distribution and describe the quantitative relationship between electric field magnitude and the spacing of equipotential surfaces.

2. 2

   Charging and Discharging a Capacitor (RC Circuit Transient)

   BI2, BI3

   Students build a resistor capacitor circuit and use an oscilloscope or voltage data logger to capture the voltage across the capacitor as it charges from zero to a supply voltage and then discharges back to zero through the resistor. The raw V versus t graph is an exponential approach and exponential decay. Students linearize the charging data by plotting ln(V final minus V) versus t, obtaining a straight line whose slope is the negative inverse of the time constant tau equals RC. They verify that the experimentally extracted tau agrees with the value calculated from the nominal R and C values. The investigation requires applying initial conditions to the general solution of the first order differential equation dQ/dt plus Q/RC equals V/R and connecting the mathematical solution to the physical circuit behavior. Sources of error include parasitic resistance in leads and the internal resistance of the voltage source.

   On the exam: Students must write and solve the RC differential equation and sketch Q(t) and I(t) with correct initial and asymptotic values in FRQ responses, precisely the skills the linearization exercise builds.

3. 3

   Kirchhoff's Laws in Multi Loop DC Circuits

   BI3

   Students construct a multi loop resistor network containing at least two independent loops and one junction, predict the current through and voltage across every element using Kirchhoff's junction rule and loop rule, then measure each quantity with a multimeter. The comparison of predicted and measured values reveals the precision of the ideal resistor model and highlights real world effects such as battery internal resistance. Students practice setting up the system of simultaneous equations that Kirchhoff's rules produce, labeling current directions, choosing loop traversal direction consistently, and applying the sign conventions for voltage rises and drops. This investigation is the foundation for all multi element circuit analysis on the exam, including circuits with capacitors in various configurations. Uncertainty estimation covers multimeter precision and resistor tolerance.

   On the exam: FRQs present a circuit diagram and ask students to write Kirchhoff's junction and loop equations and solve for unknown currents, the exact procedure practiced in this investigation.

4. 4

   Mapping the Magnetic Field of a Current Carrying Wire and Bar Magnet

   BI4

   Students use a Hall probe or compass array to map the magnetic field surrounding a long straight current carrying wire and a bar magnet, recording field direction and relative magnitude at a grid of points around each source. For the long straight wire, students plot B versus 1/r to verify the Biot Savart prediction that B is proportional to I divided by r at perpendicular distance r from an infinite straight wire. The bar magnet mapping reveals the dipole field geometry: field lines exiting the north pole and entering the south pole, with the field strength falling off faster than 1/r with distance. Students apply Ampere's law qualitatively by tracing closed paths around the wire and reasoning about the enclosed current. The investigation connects the abstract line integral of B dot dL to a physical measurement strategy using the compass or Hall probe.

   On the exam: FRQ subparts ask students to apply the Biot Savart law integral and Ampere's law to calculate the magnetic field of a long wire, solenoid, or toroid, tasks that become routine after physically mapping the field geometry in this investigation.

5. 5

   Electromagnetic Induction: Faraday's Law Verification

   BI5

   Students move a bar magnet through a solenoid connected to a galvanometer or voltage data logger and measure the induced EMF as a function of magnet speed, field strength, and number of coil turns. Faster motion, stronger field, and more turns each produce larger EMF, confirming that EMF equals negative d Phi B over dt quantitatively. Students change the sign of the induced EMF by reversing magnet direction, demonstrating Lenz's law: the induced current produces a field opposing the change in flux. The investigation builds facility with flux as a signed scalar quantity, the chain rule connecting flux change to motion, and the conceptual distinction between the rate of flux change (which determines EMF) and the total flux (which does not). Sources of error include finite galvanometer response time and fringe field effects at the coil ends.

   On the exam: FRQs give a moving conductor or changing current in a field and ask for the induced EMF magnitude using Faraday's law, the direction of induced current using Lenz's law, and the resulting force on the conductor, precisely the quantities measured and predicted in this investigation.

6. 6

   RL Circuit Time Response

   BI5

   Students build a series RL circuit with a known resistor and inductor, apply a step voltage using a signal generator or switch, and use an oscilloscope to capture the current rise from zero to its asymptotic value I max equals V/R. The current follows I(t) equals I max times (1 minus e to the negative Rt/L), and the time constant is tau equals L/R. Students linearize the data by plotting ln(I max minus I) versus t to extract tau experimentally, then compare to the value calculated from the nominal L and R. They also observe the current decay when the voltage source is removed, confirming that the inductor opposes changes in current in both directions. The investigation reinforces the mathematical analogy between RC and RL circuits while highlighting the physical difference: inductors store energy in a magnetic field, capacitors in an electric field. Students estimate L from the measured tau and the known R.

   On the exam: FRQ subparts ask students to write and solve the RL differential equation, state initial and final conditions, and sketch I(t) with the correct time constant, all tasks rehearsed directly in this investigation.

College Board requires inquiry based lab investigations throughout the AP Physics C: Electricity and Magnetism course as a condition of course authorization, but it does not mandate a fixed numbered list of investigations identical across all schools in the same way it does for some other AP science courses. Local teachers adapt the investigations to available equipment, laboratory time, and student background. The six investigations listed here represent the standard E&M laboratory curriculum aligned to the Course and Exam Description's five units. All are conducted or simulated at most authorized AP Physics C: E&M programs, and all connect directly to the experimental design subparts that appear in the three free response questions on the exam.