A uniformly charged rod of length L = 1.4 m lies along the x-axis with its right

Question

A uniformly charged rod of length L = 1.4 m lies along the x-axis with its right end at the origin. The rod has a total charge of Q = 3.2 mu C. A point P is located on the x-axis a distance a = 1.2 m to the right of the origin. Part (a) Consider a thin slice of the rod of thickness dx located a distance x away from the origin. What is the direction of the electric field at point P due to the charge on this thin slice of the rod? 25% Part (b) Write an equation for the electric field dE at point P due to the thin slide of the rod dx. Give your answers in terms of the variables O, L, x, a, dx: and the Coulomb constant, k. Notice that the coordinate x will be less than zero over the length of the rod. dE=(K(Q/L) dx)/(x + a)^2 25% Part (c) Integrate the electric field contributions from each slice over the length of the rod to write an equation for the net electric field E at point P. 25% Part (d) Calculate the magnitude of the electric field E in kilo newtons per coulomb (kN/C) at point P due to the charged rod.

Explanation / Answer

b) dE = k(Q/L)dx / (-x+a)^2

C) E = k(Q/L)*(1/a - 1/(a+L))

D) E = 9e9*(3.2e-6/1.4)*(1/1.2 - 1/2.6)

= 9231 N/C

= 9.231 kN/C

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