A uniformly charged rod rod of length 2L has a total charge +Q. The rod lies par

Question

A uniformly charged rod rod of length 2L has a total charge +Q. The rod lies parallel to the x axis, along the line y = 4L, as shown in the figure. A point P is located at the origin. NOTE: the answers should be expressed in terms of Q, L and ke. a) On the diagram, show the direction of the contribution d??E to the electric field at P from charge element dq of the rod as shown. Clearly indicate components dEx and dEy. [2.5 points] b) Without doing any calculations, determine the x component of the electric field Ex at point P due to entire rod. [2 points] c) Write an expression for the y-component dEy of the contribution to the electric field d??E at point P from the charge dq indicated in the picture. [4 points] d) Calculate the y-component of the electric field Ey at point P due to entire rod. [4 points]

Explanation / Answer

The X-component of Electric field at a point on the , dEx =-K(Q/2L)sin? dx /[x2+y2] =-K(Q/2L) dx /[x2+y2]^3/2 for total electric field , inegrating the above equation with respect from x=0 , x=2L Ex = ?-K(Q/2L) dx /[x2+d2]3/2 dx (limits from x=0 to x=2L) = -K(Q/L) [1/v(16L^2+4L^2)- 1/4L] lly, the y component of field is , Ey= -K(Q/2L) [1/4Lv(16L^2+4L^2)] Y-axis is due to small element on the conductor is given by dEy =-K(Q/2L)cos? dy /[x2+y2] =-K(Q/2L) dx /[x2+y2]^3/2

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