A ring-shaped conductor with radius a = 3. 10 cm has a total positive charge Q =

Question

A ring-shaped conductor with radius a = 3. 10 cm has a total positive charge Q = +0. 120 nC uniformly distributed around it, as shown in the figure below. The center of the ring is at the origin of coordinates O. What is the electric field (magnitude and direction) at point P, which is on the x-axis at x = 60. 0 cm? 298. 80 N/C A point charge q = -2. 00 mu C is placed at the point P described in part (a). What are the magnitude and direction of the force exerted by the charge q on the ring? -592. 6 N A ring-shaped conductor with radius a = 3. 10 cm has a total positive charge Q = +0. 120 nC uniformly distributed around it, as shown in the figure below. The center of the ring is at the origin of coordinates O. What is the electric field (magnitude and direction) at point P, which is on the x-axis at x = 60. 0 cm? 7. 3613 N/C A point charge q = -2. 00 mu C is placed at the point P described in part (a). What are the magnitude and direction of the force exerted by the charge q on the ring? 2. 06116*10**-5 N

Explanation / Answer

See using coloumbs law F = kq1*q2/r^2,
here consider a small dq charge on the ring then dE = K*dq/(x^2+a^2) along the direction line joining the dq charge and the point on central axis. But take it component
suppose your charge dq is on top ring therefore dE can be represented as = dEcos()i - dEsin()j

take the bottom most dq of ring then its magnitude will be same but direction is different i.e dE = dEcos()i - dEsin()j... adding above two u will get 2*dEcos()...

This means if you add all dq charges of ring only in x direction will be left and finally it will be E =k*q*cos()/(x^2+r^2) where q is the charge of ring

=> E = 9*10^9*.120*10^-9*cos(2.95)/(.6^2+.031^2) = 2.988i (in horizontal right direction)

now F = q*E => -2*2.988i =-5.976 N (in horizontal negative x direction)

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