Electric Field Strength Between Two Parallel Plates Problem

1. The problem statement, all variables and given/known data
If the electric field strength between two parallel plates 1cm apart is 3.1kN/C, how much energy will be used by the electric field to move an electron (placed half way between the plates) 3mm nearer to the positively charged plate?

2. Relevant equations
Work Done = 1/2V^2C

3. The attempt at a solution
I know that the answer to this question is 1.49×10^-18 J. I feel that I may be going about this question the complete wrong way but this is what I did:

I worked out the potential difference between the plates to be 31V by using the equation V=ED
V=(3.1×10^3)x(0.2×10^-2)—–> I got this value for D by taking away 3mm from the 5mm half way point between the plates.

I then subbed in the values that I know into the equation Work Done = 1/2V^2C
Work Done = 1/2 x 6.2^2 x (1.6×10^-19)
This gave me 3.08×10^-18.

I feel like I’m going the wrong way about this question. Hope someone can help and hope I’ve worded this well enough for you all to understand haha.


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