Finding an expression for Electric Potential?

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1. Mar 1, 2017

PolarBee

1. The problem statement, all variables and given/known data
There is a thin rod with charge Q that has been bent into a semicircle with radius R. Find an expression for the electric potential at the center.

Charge = Q

2. Relevant equations
V = ∫(k * dq)/r

3. The attempt at a solution
dq = λdx
λ = Q/L
L = pi * r

V = kQ / LR ∫ dx = kQ / pi * r^2 ∫ [3pi/2 - pi/2]
V = kQ/R^2

But the answer should be kQ/R. How did the other R get cancelled?

2. Mar 1, 2017

kuruman

What are your limits of integration? You should use polar coordinates and integrate over an angle.

3. Mar 1, 2017

PolarBee

I integrated from pi/2 to 3pi/2. Which came out to be just pi and that cancelled out the pi from L = pi * r.

4. Mar 1, 2017

kuruman

Your integrand has a dx in it. What did you do with it? To integrate over an angle you need a dθ in the integrand.

5. Mar 1, 2017

PolarBee

Oh I see. So dx should be rdθ instead for polar coordinates right, without it I can't integrate from pi/2 to 3pi/2?

6. Mar 1, 2017

kuruman

Correct. That cancels the extra R in the denominator. Also, note that the beginning angle is arbitrary. A semicircle is a semicircle. You might as well integrate from 0 to π.