The plastic rod at right forms a circle of radius R and has charge Q uniformly d

Question

The plastic rod at right forms a circle of radius R and has charge Q uniformly distributed along its length. Find the electric potential at the origin. Mathematical Analysis Carefully identify and label the location of the differential element on the diagram above. Carefully identify and label the location of the point of interest on the diagram above. Write an expression for dq, the charge on the differential element. Write an expression for r, the distance between the differential element and the point of interest. Write an integral expression for the electric field. Choosing limits of integration, calculate the integral.

Explanation / Answer

13) given that linear charge density is lamda = Q/L = Q/(2*pi*R)

consider a small element of ring of length dl and has charge dq

Q/(2*pi*R) = dq/dl

dq = Q*dl/(2*pi*R)

electric potential at a point on the axial line which is at a distance x from the center of the ring of origin is

dV= k*dq/sqrt(x^2+R^2)

then

due to total ring is V = integral dV

then V = integral ( k*dq/sqrt(x^2+R^2)) = k*Q/sqrt(x^2+R^2)

at the center or at the origin ,x=0

V = k*Q/R

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