Question

1. + .-5 points KatzPSEI 24-P061 My Notes Ask Your Teacher A total charge Q is distributed uniformly on a metal ring of radius R. (Use any variable or symbol stated above along with the following as necessary: k. Assume Q is positive.) 90 (a) What is the magnitude of the electric field in the center of the ring at point O (see figure above)? (b) What is the magnitude of the electric field at the point A lying on the axis of the ring a distance R from the center O (same length as the radius of the ring)? E=

Answer 1

The diagram showing the resolving of the components on a uniform metal ring is as follows: de cose r = R12 x = R R_ R The expression for the small change in the electric field is as follows: dE =ko cose Then, DE = Rp cose (x+r) Therefore,

At center, that is, at point O x=0 Then, substitute 0 for x in the equation dE = kde (x+R232 . that is, dE = kdg - (x+R22 =0 DE = 0

Therefore, E=0 Hence, the magnitude of the electric field in the centre of the ring at point O is 0.00 N/C. (6) To calculate the electric field at point. x=R Substitute R for x in the equation dE =kda — ((x+R Therefore, DE Eck JR Hence, the magnitude of the electric field at point A is k- 22r2