A rod of length L has a total charge Q uniformly distributed along its length. T

Question

A rod of length L has a total charge Q uniformly distributed along its length. The rod lies along the y axis with its center at the origin.

(a) Find an expression for the electric potential as a function of position along the x axis.

(b) Show that the result obtained in Part (a) reduces to V = kQ/|x| for |x|

Explanation / Answer

Right Answer--> pR=L ?R=L/p CHARGE ELEMENT dQ=Q/L Y AXIS ELEMENTS WILL CANCEL X AXIS ELEMENT? dE= (K dQ*dX /R^2 )*COS (T)......... dX IS LENGTH ELEMENT = R dT dT IS ANGLE ELEMENT K = 1/(4pe) T?ANGLE FROM X AXIS ? dE= ( K dQ*R dT /R^2)*COS(T) INTEGRATING FROM T? 0 TO p/2 GIVES FIELD DUE TO HALF RING MULTIPLY IT WITH 2 TO GET FULL RING E = 2* K dQ/R ? E = 2*KQ/LR?2*KQp/L^2 REPLACING K? E= 2* (Q/4eL^2)

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