Basic Electromagnetism Questions

Hohoho..

I'm back, with Physics Questions to boot.

If an uncharged parallel-plate capacitor (capacitance C) is connected to a battery, one plate becomes negatively charged as electrons move to the plate face (area A). Given that when d = 1.00pm, V = 20V, find C/A.

I'm lost. Somebody help.

AAAAaaaannnnndd:

Assume that a stationary electron is a point of charge. What is the energy density u of its electric field at radial distances (a) r = 1.00 mm, (b) r = 1.00 , (c) r = 1.00 nm, and (d) r = 1.00 pm? (e) What is u in the limit as r → 0?

Now, the answers say that u = 1/2 (vacuum permittivity) (electric field, E) ^2 ----- (1)

This reduces down to e^2/32(pi)^2(epsilon 0)r^4 ------ (2) || e is the elementary charge

I didn't know (1), so I couldn't derive (2). Instead, I tried using

u = (1/2 * C *V^2) / (4/3 * (pi) * r^3) ----- (3)

I designated V = 1/4(pi)(epsilon0) * q/r, and C = q/V but when I solved for u my answer was three times the amount.

Hence, my question is : how to I derive (1) from (3)?

If anyone can give some help, I'd very appreciative.

Cheers
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