I already got the answer wrong and it is circled in red, but I am not sure how t

Question

I already got the answer wrong and it is circled in red, but I am not sure how to find the answer. How would you find the answer showing every step of the work?

13. Consider a rectangular box that has +4.20 uC charges located at seven of its corners as shown in the figure below. Assume the length L = 3 m, the height H = 2 m, and the depth D = 1 m. Find the electric potential at the vacant corner. (7 pts.) D= 1 m H = 2 m - --- -- -- -- -- -- L = 3 m (a. V = 1.207 x 10° v dV = 2.88 x 10° v b. V = 4.26 x 10° v e. None of the above c. V = 9.28 x 10 v

Explanation / Answer

Electric potential V = kQ/r

SO electric potential at vacant corner

V = kq/L + kq/D + kq/H + kq/a + kq/b + kq/c + kq/d

where a = (H^2 +D^2)^0.5 = (1^2 + 2^2)^0.5 = 2.236 m

b = (D^2 + L^2)^0.5 = (1^2 + 3^2)^0.5 = 3.162 m

c = (b^2 + H^2)^0.5 = ((3.162)^2 + 2^2)^0.5 = 3.741 m

d = (L^2 + H^2)^0.5 = (3^2 + 2^2)^0.5 = 3.605 m

=> V = 9*10^9*4.2*10^-6*[ 1/3 + 1/1 + 1/2 + 1/2.236 + 1/3.162 + 1/3.741 + 1/3.605 ] = 118.72*10^3 volt

=> V = 1.187*10^5 volt  

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