Question

RC-0 A line of total charge Q is evenly distributed around a ring of radius R. The center of the ring is at the origin and the ring lies in the x-y plane as shown below. a) Explain why Enety-0 at point P for the entire ring. In your explanation, discuss the effect of charge, distance, and angle. Use the figure above to clearly shown any charges, distances, and angles used in your discussion. b) Describe dE, for the dq shown below. Clearly show on the figure below each angle and distance used in your equation for dEx c) Set up an integral BUT YOU WON'T BE ABLE TO INTEGRATE to find Enetx- Show the limits of the integral. d) Name the variables in part b) that change as your integral variable changes.

Answer 1

because cos theta = d/r cos theta = d/squareroot R^2 + d^2 A conducting ring of radius R has a total charge q uniformly distributed over its circumference. The electric field at point p that lies on the axis of the ring at a distance d from its centre. We divide the ring into infinitesimal segments of length dl. Each segment has charge dq and acts as a point charge square of electric field. Let dE^vector be the electric field from one such segment the net electric field at p is then the sum off all contributions dE^vector from all the segments that make up the ring. If we consider two ring segments at the top and bottom of the ring, we see that the contributions dE^vector to the field at p from those segments have the same x - component but opposite y - components In y - direction we find out opposite components. Hence, the total y - component of field due