Chapter 1 Problems
Original chapter problems, with explicitly stated assumptions and authored solutions. These retain the manuscript’s problem identities; calculus extensions and unfinished material make no AP coverage claim.
Original problem 1
Optional original-source extension. Prerequisites: vector addition, trigonometry and regular-pentagon geometry. This item makes no AP coverage claim.
Five identical point charges q are fixed at the vertices of a regular pentagon inscribed in a circle of radius R. Find the force on one charge and its initial direction of motion if released from rest.
Authored clarification: All five charges have the same signed charge; the circle radius is R and all positions are fixed while computing the instantaneous force.
Worked solution with reasons for each step · Original reading location
Archived original prompt
No original chapter-problem answer was supplied. This worked solution is authored for the explicitly stated reviewed prompt.
Original problem 2
Explain superposition and show from Coulomb’s law that electric fields add vectorially.
Authored clarification: Use classical electrostatics with fixed source charges; the test charge does not disturb them.
Worked solution with reasons for each step · Original reading location
Archived original prompt
No original chapter-problem answer was supplied. This worked solution is authored for the explicitly stated reviewed prompt.
Original problem 3
A prescribed electric field is . Find the force on a point charge q at (x,y).
Authored clarification: A and B are constants with units chosen so each field component has units N/C. This prescribed field need not be electrostatic when B≠0.
Worked solution with reasons for each step · Original reading location
Archived original prompt
No original chapter-problem answer was supplied. This worked solution is authored for the explicitly stated reviewed prompt.
Original problem 4
Optional original-source extension. Prerequisites: point-charge vector fields and coordinate geometry. This item makes no AP coverage claim.
Protons are at (a,−a) and (−a,a), while electrons are at (a,a) and (−a,−a). With a=1 m, describe the field-line pattern and give the electric field at an arbitrary point (x,y) away from a charge.
Authored clarification: Coordinates are in metres; particles are fixed ideal point charges ±e. Field lines are a qualitative representation of the vector sum, not particle trajectories.
Worked solution with reasons for each step · Original reading location
Archived original prompt
No original chapter-problem answer was supplied. This worked solution is authored for the explicitly stated reviewed prompt.
Original problem 5
Optional original-source extension. Prerequisites: continuous line charge, trigonometric components and a definite integral. This item makes no AP coverage claim.
A thin wire forms the upper semicircle x²+y²=R², y≥0 and carries uniform total charge Q. Find the field at its center.
Authored clarification: The original omits the charge distribution. Here it is uniform, the length is L=πR, and Q is explicitly supplied.
Worked solution with reasons for each step · Original reading location
Archived original prompt
No original chapter-problem answer was supplied. This worked solution is authored for the explicitly stated reviewed prompt.
Original problem 6
Optional original-source extension. Prerequisites: reflection symmetry, continuous surface charge and a double integral; the closed-form evaluation is supplied. This item makes no AP coverage claim.
A square thin plate of side L in the xy plane has uniform total charge Q. Find its electric field on the positive z axis at height h>0.
Authored clarification: The observation point is above the center, not an arbitrary off-axis point. Edge effects are included by integrating the finite square.
Worked solution with reasons for each step · Original reading location
Archived original prompt
No original chapter-problem answer was supplied. This worked solution is authored for the explicitly stated reviewed prompt.
Original problem 7
Two infinite nonconducting sheets at x=0 and x=d have uniform surface densities σ₁ and σ₂. Find the field between them for (a) σ₁=σ₂=σ and (b) σ₁=σ, σ₂=−σ.
Authored clarification: The sheets are ideal infinite nonconductors in vacuum; σ is positive when identifying directions.
Worked solution with reasons for each step · Original reading location
Archived original prompt
No original chapter-problem answer was supplied. This worked solution is authored for the explicitly stated reviewed prompt.
Original problem 8
Optional original-source extension. Prerequisites: cylindrical symmetry, continuous volume charge and Gauss’s law. This item makes no AP coverage claim.
An infinitely long insulating cylinder has radius R and uniform volume charge density ρ. Find its radial electric field at distance s from its axis, inside and outside.
Authored clarification: A finite total q is unsuitable for an infinite source. The chosen model is a uniform insulating cylinder; a conducting cable would have zero interior field at electrostatic equilibrium.
Worked solution with reasons for each step · Original reading location
Archived original prompt
No original chapter-problem answer was supplied. This worked solution is authored for the explicitly stated reviewed prompt.