An insulating rod of length l is bent into a circular arc of radius R that subtends an angle theta from the center of the circle. The rod has a charge Q ditributed uniformly along its length. Find the electric potential at the center of the circular arc.(adsbygoogle = window.adsbygoogle || []).push({});

Struggling with this problem.

I know that I have to divide the charge Q into many very small charges, essentially point charges, then sum them up (integration).

dV = dq/(4 Π Ε0 R)

Length of dq = ds

db = angle subtended by ds

dΒ=ds/R => ds = dBR

dq = λds => dq = λdBR

V = ∫ dq/(4 Π Ε0 R)

V = ∫ λdBR/(4 Π Ε0 R)

Now, this is where it all goes wrong for me.

I take out the constants V = λR/(4 Π Ε0 R) * ∫ dB

My Rs cancel out, which makes no sense.

The radius must be important in the calculation of the difference potential.

Notice also that I did not indicate the limits on the integration. In a similar problem which was done in a previous assignemnt to calculate the electric field at the center, the upper and lower limits were set to -B/2 and B/2, but I am not sure why.

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# Electric potential at center of circular arc

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