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Chapter 25: Q. 73 (page 713)

The wire in FIGURE P25.73 has linear charge density 位. What is the electric potential at the center of the semicircle?

Short Answer

Expert verified

The electric potential at the center of the semicircle isV=k位(2In(3)+蟺).

Step by step solution

01

Given Information

We need to find the electric potential at the center of the semicircle.

02

Simplify

The potential at the point of interest will be the sum of potentials coming from the straight lines and the curved section. By symmetry, it is clear that the potential coming from the two straight segments are equal. So, we can calculate one of them, and the potential coming from both will be twice in our result.

Therefore, we can write

V=k2鈭�02R位dzx+R+鈭�0蟺搁位dxR

Factorizing the linear charge density, we can simplify

V=k位鈭�02Rdxx+R+1R鈭�0蟺搁dx

The result will be

k位2In3R-InR+蟺=k位2In3+蟺

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