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Midterm Exam Review: Electric Fields, Charged Plates, and Circuit Calculations

This midterm exam focuses on key concepts in electrostatics and circuits for PHYS 1304. It includes problems relating to point charges, electric fields between charged plates, and circuit analysis. Students are required to find points of zero electric field between charges, compute work done in moving a charge, analyze electric fields in and between insulating plates, and assess circuit behavior and energy storage in capacitors. Make sure to prepare for each section to optimize your score.

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Midterm Exam Review: Electric Fields, Charged Plates, and Circuit Calculations

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  1. PHYS 1304 Mid-term Exam Name ID • (Total 30 points) Two point charges, q1 and q2, are fixed in space. The distance between the two charges is d. Here q1 = 2.0 μC, q2 = 8.0 μC, and d = 9.0 cm. 1 μC = 10-6 C. (a, 20 points) Find the point in space that is close to the two charges where the electric field is 0. (b, 10 points) Now you move a charge q3 from infinitely far away to this point, how much work you have to do during this process when q3 = 1.0 μC? The Coulomb constant ke = 8.99×109 N·m2/C2. (c, bonus 5 points, do it when you have time in the end) Is q3 in a stable or unstable equilibrium condition? Would your answer change if q3 = -1.0 μC?

  2. PHYS 1304 Mid-term Exam Name ID • (30 points) Two infinitely large plates made of insulating material (ignore its dielectric property) are placed distance D apart, parallel to each other. The thickness of each plate is d. One plate has a volume charge density ρ(assuming positive charge), the other -ρ. Here D = 10.0 mm, d = 1.0 mm, and ρ = 1.0 μC/mm3. (a, 20 points) Find the electric field (magnitude and direction) between the two plates (excluding the plates volume) (b, 10 points) Find the electric fields (magnitude and direction) inside the plates, as a function of distance from the center of the plates. The permittivity of free space εo = 8.85×10-12 C2/N·m2.

  3. PHYS 1304 Mid-term Exam Name ID • (40 points) A circuit shown in the figure where the switch has been closed for a long time. Find (a, 20 points) the current through each resister, (b, 5 points) the power consumed by the 4.0 ohm resistor, (c, 5 points) the energy stored in the capacitor. (d, 10 points) If we start the time when the switch S is thrown open (this is the moment when t0 = 0), calculate the current in each resistor as a function of time t, with t ≥ 0. 24.0V 4.0Ω 2.0 μF S 2.0Ω 6.0Ω 10.0V 6.0Ω

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