- #1

rbrayana123

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## Homework Statement

Consider a black box which is approximately a 10-cm cube with two binding posts. Each of these terminals is connected by a wire to some external circuits. Otherwise, the box is well insulated from everything. A current of approximately 1 amp flows through the circuit element. Suppose now that the current in and the current out differ by one part in a million. About how long would it take, unless something else happens, for the box to rise in potential by 1000 volts.

## Homework Equations

Q = CV

V = IR

-dQ/dt = I

## The Attempt at a Solution

I'm not exactly sure how to start off this problem. I'm not given the details of the external circuit; nor can I figure out the capacitance of the cube (if that's relevant at all). Here's my attempt though:

Assuming the cube is a conductor, I can calculate out the electric field at the surface using Gauss' Law:

6EA = Q/[itex]\epsilon[/itex]

_{o}, where A is the area of one side.

E = Q/[itex]\epsilon[/itex]

_{o}6A

However, if I integrate from 0.05 m to infinity, I get an infinite potential. I'm guessing the electric field musn't be constant outside of the cube.

I threw that out of the bag, so I tried calculating the rate at which current changes... except, I don't know how much time it takes to traverse the entire circuit. All I know is that it changes by a factor of (1 - 10^-6) so dI/dt = I(1 - 10^-6), except maybe with some factor of time in there.