Q x 2L L P x A very thin non-conducting ring of radius R carries a...

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Q x 2L L P x A very thin non-conducting ring of radius R carries a positive charge Q uniformly distributed on it. The ring lies on the y-z plane with its center at the origin O. A uniformly charged non-conducting rod of length L with an identical positive charge Q lies on the x-axis with one end at x=2L and the other end at x=3L. The point Plies on the x-axis between the two objects, a distance from the origin. Choose the zero point for the electric potential to be at infinity, V (oa) = 0. Express your answers to the following questions using some or all of the following: epsilon_0 for eg, Q, x, R, L,q, hati for 1. (Part a) Determine the electric potential V (P) at the point P. V (P) = (Part b) Determine a vector expression for the electric field (2) at the point P. (P) = (Part c) Suppose a charge q is moved from infinity to the origin (= 0, center of the ring). What is the change in potential energy of the system? AU U (0) U(0) = You may find this integral table useful. doe = a-x dx (a-x) da (a-x) - = In (a) 1 1 -x) 2(a-x) dx (a + x2)1/2 dx (a + x2)8/2 xdx (a +22)8/2 = In (x + (x + a)) 1 CCC = a (a+52)1/2 1 (a + x2)1/2 Q x 2L L P x A very thin non-conducting ring of radius R carries a positive charge Q uniformly distributed on it. The ring lies on the y-z plane with its center at the origin O. A uniformly charged non-conducting rod of length L with an identical positive charge Q lies on the x-axis with one end at x=2L and the other end at x=3L. The point Plies on the x-axis between the two objects, a distance from the origin. Choose the zero point for the electric potential to be at infinity, V (oa) = 0. Express your answers to the following questions using some or all of the following: epsilon_0 for eg, Q, x, R, L,q, hati for 1. (Part a) Determine the electric potential V (P) at the point P. V (P) = (Part b) Determine a vector expression for the electric field (2) at the point P. (P) = (Part c) Suppose a charge q is moved from infinity to the origin (= 0, center of the ring). What is the change in potential energy of the system? AU U (0) U(0) = You may find this integral table useful. doe = a-x dx (a-x) da (a-x) - = In (a) 1 1 -x) 2(a-x) dx (a + x2)1/2 dx (a + x2)8/2 xdx (a +22)8/2 = In (x + (x + a)) 1 CCC = a (a+52)1/2 1 (a + x2)1/2