You\'ve built a capacitor using two metal plates that you know have an area of 0

Question

You've built a capacitor using two metal plates that you know have an area of 0.055 m2, but you've forgotten how far apart they are. To test this, you connect the capacitor to a power supply providing a voltage of 10.3 V (remember, if you don't know something about an electronic component, your best option is to hook it up to electricity!). You are able to perform some tests to identify that you have stored 3.6 nJ of energy when you do this. Based on these experiments, what is the separation (in mm) between the plates?

Explanation / Answer

E = 0.5CV^2

3.6*10^-9 = 0.5*C*10.3^2

C = 6.78*10^-11

C = Aeo / d

6.78*10^-11 = 0.055*8.85*10^-12 / d

d = 0.007 m

so the seperation is 7 mm

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