Problem 12: 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 = 8.2 μC. A point P is located on the x-axis a distance a = 1.8 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? 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 Q, 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. 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. Part (d) Calculate the magnitude of the electric field E in kilonewtons per coulomb (kN/C) at point P due to the charged rod.
Problem 12: 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 = 8.2 μC. A point P is located on the x-axis a distance a = 1.8 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?
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 Q, 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.
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.
Part (d) Calculate the magnitude of the electric field E in kilonewtons per coulomb (kN/C) at point P due to the charged rod.
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