Question

Consider a wire in the shape of a semi-circle of radius R, with a total positive net charge Q vistributed over the wire uniformly. Divide the wire into at least 8 equal point-like “chunks” of charge. Then, for each “chunk,” sketch (on the same diagram) the E-field vector that bit of charge would cause at the center of the (semi-) circle.
Explain, using this picture, how each “chunk’s” field contributes to the net field at that center point.
Would a full circle of charge double the net field at the center? Explain.

Answer 1

I cant do the sketch. Notice the E is in directions, which the vertical will cancel out, and you are left with a net horzontal (to the axis of symettry) component.
Given that, a full circle would then cancel that out, and E at the center would be zero.

Now, all that is true in the Plane of the semicircle. However, above and below the that plane, it is not true, there will be a component in the z direction on each side of the plane. Think about that (pretend instead of the wire, you had a disk of charge)...