Question

Two 11-cm-diameter metal plates 1.4 cm apart are charged to ±12.5 nC. They are suddenly connected together by a 0.224-mm-diameter copper wire stretched taut from the center of one plate to the center of the other.

Part A

What is the maximum current in the wire?

Express your answer with the appropriate units.

Part B

Does the current increase with time, decrease with time, or remain steady?

Increase with time?

decrease with time?

remain steady?

Part C

What is the total amount of energy dissipated in the wire?

Express your answer with the appropriate units.

Answer 1

A) Parallel plate cap
C = ε₀εr(A/d) in Farads
ε₀ is 8.8542e-12 F/m
εr is dielectric constant (vacuum = 1)
A and d are area of plate in m² and separation in m

C = (8.85e-12)(π(0.055)²/(0.014)) = 6.01e-12 = 6.01 pF

Q = CV
V = 12.5 nC/6.01 pF = 2080.7 volts

current in wire is limited only by it's resistance

Resistance of a wire in Ω
R = ρL/A
ρ is resistivity of the material
L is length in meters
A is cross-sectional area in m²
A = πr², r is radius of wire in m
resistivity Cu 17.2 (nΩ-m)

R = 17.2e-9(0.014)/(π(0.000224)²) = 0.0015 ohm

I = E/R = 2080.7 / 0.0015 = 1.39e+6 amps.

very high, but the amount of energy is very low due to the low value for C


B) it decreases with time, as the C discharges.

C) E = ½CV² Energy in a cap
E = ½(6.01pF)(2080.7)² = 0.000013 J