. Consider a positive uniformly charged half ring with total charge Q and radius
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Question
. Consider a positive uniformly charged half ring with total charge Q and radius of curvature R, positioned symmetrically about the y-axis as shown. a) Due to the symmetry in this situation, the electric field at any point on the z-axis will have components in what directions? b) Write an expression for dE for a point on the z-axis. c) Write an expression for the components of dE in all directions necessary from (a) d) Using the appropriate substitution for dQ, solve for each of the components of dE from (c).Explanation / Answer
as per perpendiculrity nature between electric field , magnetic and propogation vector ,then the electric field at any point on z axis will have a horizontal component alonf z axis and vertical component parallel o y axis.
b) using gauss theorem E= q/ e0 dA cosp ; where q = charge present, e0=permitivity of free space value , p=angle subtended by a point on ring to any point on axis
dA is the surface area of given semi circular structure= 3.14 x r ; where r= radius
but due to symmetry condition dA =2 x 3.14 x r
finally , E = dq/e0 2x3.14xr cosp
now value of cosp= z/sqrt(z2 + r2) where z is distance of a certain point on z axis
now dq= (E X 2X 3.14 X sqrt(z2 + r2)) / z
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