A physics teacher tries to build a device that illustrates Maxwell\'s generaliza

Question

A physics teacher tries to build a device that illustrates Maxwell's generalization of Ampere's law. She drills a hole in the center of each plate of a parallel-plate capacitor and then runs a wire through the holes (Figure 1). There is no connection between the wire and the plates, and the potential difference across the plates can be controlled.

(A)

In particular what must be the rate of change of the potential difference if she wants no magnetic field at a distance r = 20 mm from the wire when it carries a steady current of 0.0400 A and the distance between the plates is d = 3.0 mm ?

Explanation / Answer

Remember and apply for parallel plate caapcitor, these as formulas

1. Capacitance C = K eoA/d

where K is dieelctric constant   ( for air K = 1)

eo is permnittivity constant = 8.85 e-12

A is area = pi^2   ( for circular plates)    and   l* b   for rectanular plates

and

d is the distance between the plates

electric field between the plates is E = Q/eo A

( also given by E = V/d) and as i = Q/t

E = it/eo A

V/d   = it /eoA

V/t = id /eo A

V/t = 0.04 * 3e -3/(8.85 e-12 * 3.14 * 0.02 * 0.02)

dV/dt = 1.079 *10^10 V/s

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