Question

A 4.0-cm-diameter parallel-plate capacitor with a 1.0 mm spacing is charged to 1000 V. A switch closes at t =0s, and the capacitor is discharged through a wire with 0.20Ω resistance.

Part A

Find an expression for the magnetic field strength inside the capacitor at r=1.0cm as a function of time t (where t is in ps).

Express your answer in terms of t.

A. B(t) = ___T

Part B

Draw a graph of B(T) versus t(ps).

Answer 1

The capacitance of the capacitor is, (8.85x10-12 Fm): π( diameter 1.0x10' m -2 4.0x10 m =1.11x10-11 F The Current across the capacitor at any time is, 1000 V020 LIL10F 0.2Ω = 5000 e-2.2210, A = 5000 e-222pA The magnetic field between the plates is, diam eter 2r(diameter) Plug in the values 2(4TX10. T-m/A)| 5000e-222 ps A |(1.0×10-2 m) B (t) 27(4.0x102 m) = (0.025) e-222 T The magnetic field decays exponentially as time passes