# The value of electric current on a sinking conductor

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1. May 15, 2016

### darkprior

1. The problem statement, all variables and given/known data
A flat capacitor formed by two square plates of side 0.3 m which are 2 mm apart. Source keeps voltage 250 V on the plates. What current flows between the plates and the source if the condenser is immersing in kerosene at velocity of 5 mm / s? The relative permittivity of kerosene is 2.

2. Relevant equations
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3. The attempt at a solution
Here is a pic

I=Q/t

Because of the fact that immersing cunductor can be understood as two parallel conductors the capacity of an immersed conductor (the depth x = v*t) is C =(ε0*(a-x)*a)/d + (ε0εr*a*x)/d

My question is how do I compute the time in the x = v*t? And sorry for my english.

2. May 15, 2016

### vela

Staff Emeritus
The simple answer is you don't. Just assume you know it and hope it cancels out in the end.

3. May 15, 2016

### darkprior

But it doesn't cancel in the end because of the plus and minus in the equation

4. May 15, 2016

### vela

Staff Emeritus
What equation? Remember your ultimate goal is to find the current.

5. May 15, 2016

### darkprior

I think I get it now...

I put the "v*t" instead the "x" in the equation for capacity, multiply it by the voltage (U) and then derivate it following I=dQ/dt

Or am I wrong?

Anyways thank you for your clear explanation, it helped me a lot

Last edited: May 15, 2016
6. May 15, 2016

### vela

Staff Emeritus
That's right. Or you could just leave it as $x$, and when you differentiate with respect to time, you'll get $v$ in its place.

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