AP Physics Physics: Electricity & Magnetism 4 — Questions and Answers
Question 1: An RC circuit has resistance R and capacitance C. The time constant τ represents the time for the capacitor to charge to approximately what fraction of its maximum charge?
- 50%
- 63% (Correct answer)
- 86%
- 99%
Correct answer: 63%
After one time constant τ = RC, the charge reaches Q₀(1 − e⁻¹) ≈ 0.632 Q₀, or about 63% of maximum.
Question 2: A uniform electric field E points in the +x direction. The electric potential V decreases most rapidly in the:
- +y direction
- −y direction
- +x direction (Correct answer)
- −x direction
Correct answer: +x direction
The electric field points in the direction of greatest decrease in potential, so potential decreases most rapidly in the +x direction (direction of E).
Question 3: Which Maxwell equation describes the fact that magnetic monopoles do not exist?
- ∇·E = ρ/ε₀
- ∇·B = 0 (Correct answer)
- ∇×E = −∂B/∂t
- ∇×B = μ₀J + μ₀ε₀∂E/∂t
Correct answer: ∇·B = 0
∇·B = 0 (Gauss's Law for magnetism) states that the net magnetic flux through any closed surface is zero, implying no magnetic monopoles.
Question 4: A wire of length L carrying current I is placed in a uniform magnetic field B perpendicular to the wire. The magnitude of the force on the wire is:
- BIL²
- BIL (Correct answer)
- BI/L
- B²IL
Correct answer: BIL
The force on a current-carrying wire is F = BIL sin θ; with θ = 90°, F = BIL.
Question 5: Two capacitors C₁ = 3 μF and C₂ = 6 μF are connected in series. The equivalent capacitance is:
- 9 μF
- 2 μF (Correct answer)
- 4.5 μF
- 18 μF
Correct answer: 2 μF
For series capacitors: 1/C_eq = 1/3 + 1/6 = 1/2, so C_eq = 2 μF.
Question 6: The displacement current in Maxwell's equations was introduced to:
- Account for resistance in vacuum
- Ensure continuity of the magnetic field at conductor boundaries
- Correct Ampère's Law so that it satisfies charge conservation (Correct answer)
- Explain the photoelectric effect
Correct answer: Correct Ampère's Law so that it satisfies charge conservation
Maxwell added the displacement current term ε₀∂E/∂t to Ampère's Law to ensure that ∇·J + ∂ρ/∂t = 0 (charge conservation) is satisfied.
Question 7: A charged particle enters a region with crossed electric and magnetic fields (E perpendicular to B). For the particle to travel in a straight line, its speed must be:
- v = EB
- v = E/B (Correct answer)
- v = B/E
- v = √(EB)
Correct answer: v = E/B
For straight-line motion, the electric and magnetic forces must balance: qE = qvB, giving v = E/B.
AP Physics Physics: Electricity & Magnetism 4
An RC circuit has resistance R and capacitance C.
The time constant τ represents the time for the capacitor to charge to approximately what fraction of its maximum charge?