Question

Asked Oct 22, 2019

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A wire having a uniform linear charge density *λ* is bent into the shape shown in the figure below. Find the electric potential at point *O*. (Use the following as necessary: *R*, *k** _{e}* and

Step 1

Find the electric potential at the center *O* due to semicircular region as

The expression for the charge *dQ *present on the small element having length *dS * is,

Step 2

Here *λ* is the line charge density

The length of arc subtended from the center is given by,

*dS* = *λdθ*

Substituting this expression for *dS *in the expression for *dQ* and write the expression for the electric potential at the center *O* due to the small segment of length as,

Step 3

The expression for the total potential due to semi-circular section of wire at *O* is,

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