A semi-circular, insulating rod has radius R and lies in the xy-plane. It carries a total charge Q.
A semi-circular, insulating rod has radius R and lies in the xy-plane. It carries a total charge Q. The center of curvature (i.e., the center of the circle of which this is a part) is at the origin, and the rod itself is in the first and second quadrants. Find the electric field vector produced by this charge distribution at the origin.
Homework Answers
Let us draw the diagram from the description of the problem
:
The electric field due to the infinitesimal element 
at
the origin is
corresponding to this element there lies another element of the symmetrically opposite side of the y-axis. the electric field in the y-axis is exactly equal and opposite and hence is cancelled out, however, due to this symmetrically opposite element also, the electric field along the x-axis is same.
Hence the net electric field due to all such infinitesimal elements will be only along -ve x-direction.
Hence we only need to calculate the field along the negative x-direction
Here
Hence
[we will integrate over 
from 0 to
]
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A semi-circular, insulating rod has radius R and lies in the xy-plane. It carries a total charge Q.
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