A charge of - 5.50 {nC} is spread uniformly overthe surface of one face of a non

Question

A charge of - 5.50 {nC} is spread uniformly overthe surface of one face of a nonconducting disk of radius1.25 {cm}.Find the magnitude of theelectric field this disk produces at a point P on the axis of the disk a distance of3.00 {cm} from its center.Supposethat the charge were all pushed away from the center anddistributed uniformly on the outer rim of the disk. Find themagnitude of the electric field at point P.If the charge is all brought to the center of thedisk, find the magnitude and direction of the electric field atpoint P.Why is the field in part (a)stronger than the field in part (b)? Why is the field in part (c)the strongest of the three fields?

Explanation / Answer

Given :    For a uniformly charged ring E = Q x / (4 o (x2 +a2)3/2) where Q is total charge onring E = -(9 * 109 * 5.50 * 10-9 * 0.03) / (0.01252 + .032 )3/2     = - 1.485 / 2.08 *10-5     = -3.4 * 105 N/C a = radius and x = distance from center If all of the charge is at the center then E = Q / (4 0 / x2)    and the field is directed axiallytowards the center of the disk since electric field lines end onnegative charges For a uniformly charged ring E = Q x / (4 o (x2 +a2)3/2) where Q is total charge onring E = -(9 * 109 * 5.50 * 10-9 * 0.03) / (0.01252 + .032 )3/2     = - 1.485 / 2.08 *10-5     = -3.4 * 105 N/C a = radius and x = distance from center If all of the charge is at the center then E = Q / (4 0 / x2)    and the field is directed axiallytowards the center of the disk since electric field lines end onnegative charges

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