Gauss's law test with answers for AP Physics C (free PDF download)

Quick answer: Electric flux is Φ = ∮E · dA, the field passing through a surface. This AP Physics C test on gauss's law has 8 questions worth 20 marks, to do in 45 minutes: flux through a tilted area, net flux and inside a conductor. The mark scheme is on a separate page; free printable PDF.

This test covers flux, Gauss’s law and fields of continuous charge distributions in the style of AP Physics C: Electricity and Magnetism. Show every step, name the Gaussian surface where you use one, and give units. Take k = 8.99 × 10⁹ N m²/C² and ε₀ = 8.85 × 10⁻¹² C²/(N m²). The total is 20 marks.

Level: AP Physics C (Mechanics and E&M, calculus-based) · Curriculum: AP PC:E&M Unit 8

Time: 45 minutes · 8 questions · Total: 20 marks · Calculator allowed

Contents

Question 1 Flux through a tilted area (2 marks)

A uniform field of 800 N/C passes through a flat surface of area 0.30 m². The normal makes 30° with the field. Calculate the flux.

Question 2 Net flux (3 marks)

A closed surface encloses +5.0 nC and −2.0 nC.

Calculate the net flux through it. (2 marks)
State the effect on the net flux of adding a +4.0 nC charge outside the surface. (1 mark)

Question 3 Inside a conductor (2 marks)

Explain why the electric field inside a conductor in electrostatic equilibrium is zero and where any net charge is found.

Question 4 Line of charge (3 marks)

Question 4: Gaussian cylinder around a line charge.

Use Gauss’s law and the cylinder in the figure to derive the field at distance r from a very long line of charge with linear density λ.

Question 5 Insulating sphere (3 marks)

A solid insulating sphere of radius 0.060 m carries a uniform +9.0 nC. Calculate the field at r = 0.030 m and at r = 0.12 m.

Question 6 Charged ring (3 marks)

A thin ring of radius 0.40 m carries +6.0 nC. Calculate the field on its axis 0.30 m from the centre and explain why the perpendicular components cancel.