A thin ring with radius R is placed on the xy plane. The line charge density...

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A thin ring with radius R is placed on the xy plane. The line charge density on the ring is fixed and distributes as a sin op (where > 0 and the op is the counterclockwise rotational angle from the +x direction). a) Draw a 2D sketch of the ring on the xy plane, and indicate which side of the ring carries positive charge. b) Calculate the electric dipole moment vector of the ring. c) Treat the ring as a dipole. In spherical coordinates, define the direction of the polar axis, then write down the electric potential at an arbitrary point that is at a distance r from the origin (r>R). Express your result as a function of , R, r, 0 (Do NOT use vectors p or in your result.) d) Treat the ring as a dipole. In Cartesian coordinates, write down the electric field vector at a point (x, y, z) that is much farther from the origin than R. Express your result as a function of A, R, x, y, z. (Do NOT use vectors p or in your result.) A thin ring with radius R is placed on the xy plane. The line charge density on the ring is fixed and distributes as a sin op (where > 0 and the op is the counterclockwise rotational angle from the +x direction). a) Draw a 2D sketch of the ring on the xy plane, and indicate which side of the ring carries positive charge. b) Calculate the electric dipole moment vector of the ring. c) Treat the ring as a dipole. In spherical coordinates, define the direction of the polar axis, then write down the electric potential at an arbitrary point that is at a distance r from the origin (r>R). Express your result as a function of , R, r, 0 (Do NOT use vectors p or in your result.) d) Treat the ring as a dipole. In Cartesian coordinates, write down the electric field vector at a point (x, y, z) that is much farther from the origin than R. Express your result as a function of A, R, x, y, z. (Do NOT use vectors p or in your result.)