Positive electric charge Q is distributed uniformly along a line in the shape of a semicircle...

Positive electric charge Q is distributed uniformly along a line in the shape of a semicircle of radius R lying in the upper half of the coordinate plane. Find the electric potential at the origin.

Solutions

Expert Solution

Total length of the semicircle is

Given charge Q is uniformly distributed, the linear charge density of the wire is

Consider the wire to be made of small charge elements of angular width . Consider one such element at angle as shown in the figure. The length of this charge element is . The charge on this element is

This element can be considered as a point charge. The electric potential of a point charge q at a distance r away from the charge is V=kq/r where . Therefore, the electric potential of the charge element is

To find the electric potential due to all such small elements of the wire, we integrate over these small elements.

genius_generous answered 1 year ago

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