In: Physics
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.
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.