Section 4.10: Chapter 4 Test — Electric Fields & Potential

This test checks understanding of electric fields, Coulomb’s law, electric potential & potential energy, equipotentials, motion of charges, and capacitance. Answer all questions; show full workings where required. Use \(k=9.0\times10^9\) N·m²/C² and \(e=1.602\times10^{-19}\) C where needed.

Part A — Short Answer / Calculations (show working)

  1. Two point charges, \(q_1=+4.0\ \mu\text{C}\) and \(q_2=-2.0\ \mu\text{C}\), are separated by 0.50 m. Calculate the magnitude and direction of the force on each charge.
  2. Find the electric field at point P located 0.30 m from a point charge \(Q=+6.0\ \mu\text{C}\).
  3. A test charge \(q_t=2.0\ \mu\text{C}\) experiences an electric force of \(0.10\ \text{N}\). Determine the electric field at the test charge and the potential at its location if potential energy of the test charge there is \(1.0\ \text{J}\).
  4. Calculate the electric potential energy of a system of two charges \(+3\ \mu\text{C}\) and \(+5\ \mu\text{C}\) separated by 0.40 m.
  5. Determine the work required to move a \(+1.0\ \mu\text{C}\) charge from point A (potential 25 V) to point B (potential -15 V).

Part B — Conceptual / Short Explanation

  1. Explain why the electric field is always perpendicular to equipotential surfaces. (2–3 sentences)
  2. Describe qualitatively how the trajectory of an electron differs from that of a proton when both enter the same uniform electric field with identical initial velocities.
  3. State and briefly explain how adding a dielectric between the plates of a capacitor affects: (a) capacitance, (b) stored charge (if connected to battery), and (c) energy stored. Assume battery remains connected in (b) and (c).

Part C — Multi-step Problems

  1. A parallel-plate capacitor has plate area \(A=0.025\ \text{m}^2\) and separation \(d=1.0\ \text{mm}\). (a) Calculate its capacitance in vacuum. (b) If connected to a 12 V battery, find the stored energy. (c) If a dielectric with \(\varepsilon_r=5\) is inserted while still connected, compute the new stored energy.
  2. A proton is accelerated from rest through a potential difference of 500 V. (a) Calculate its kinetic energy in joules and electron-volts. (b) Determine its speed just after acceleration (non-relativistic approximation is acceptable).
  3. Three charges lie on a line: \(+2\ \mu\text{C}\) at x=0, \(-3\ \mu\text{C}\) at x=0.6 m, and \(+1\ \mu\text{C}\) at x=1.0 m. (a) Find the net electric field at x = 0.4 m. (b) Compute the electric potential at x = 0.4 m (take V→0 at infinity).

Part D — Challenge / Extension (optional, for extra credit)

  1. A particle of mass \(2.0\times10^{-3}\ \text{kg}\) carries charge \(+5.0\times10^{-6}\ \text{C}\). It is released from rest in a uniform electric field of magnitude \(200\ \text{N/C}\) directed horizontally. Neglect gravity. (a) Find its acceleration. (b) After moving 0.10 m, what is its kinetic energy and speed? (c) If this particle instead carried opposite sign charge of same magnitude, describe qualitatively the motion.

Instructions: show all steps, write units, and keep 2–3 significant figures where appropriate. Use algebraic forms before numerical substitution where possible. Good luck!

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