A finite rod of length L has total charge q, distributed uniformly along its len

Question

A finite rod of length L has total charge q, distributed uniformly along its length. The rod lies on the x -axis and is centered at the origin. Thus one endpoint is located at (L/2,0), and the other is located at (L/2,0). Define the electric potential to be zero at an infinite distance away from the rod. Throughout this problem, you may use the constant k in place of the expression 1 / 40.

Part A

(Figure 1)
What is VA, the electric potential at point A (see the figure), located a distance d above the midpoint of the rod on the y axis?

Express your answer in terms of L, d, q, and k.

Part B

What is VB, the electric potential at point B, located at distance d from one end of the rod (on the x axis)?

(Figure 2)

Give your answer in terms of q, L, d, and k.

If someone could please show me step by step how to get the answer that would be great. I seem to be confused on what equations to even start using

Thanks!

Explanation / Answer

Electric potential has no direction

dV=Kdq/r

dq=Qdx/L

dV=KQdx/Lr

r^2=x^2+d^2

dV=Kqdx/L(x^2+d^2)^0.5

V=integrate x=-L/2 to x=L/2

Part B

dV=Kqdx/Lr

dx=dr since same direction

V= integrate r=L+D to r=D

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