An infinite line of positive charge lies along the y axis, with charge density λ = 1.90 μC/m. A dipole is placed with its center along the x axis at x = 26.0 cm. The dipole consists of two charges ±10.0 μC separated by 2.00 cm. The axis of the dipole makes an angle of 45.0° with the x axis, and the positive charge is farther from the line of charge than the negative charge. Find the net force exerted on the dipole.

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…

A solid core carrying excess charge, Q = 46.4 μC, is located at the center of concentric spherical shells. The two spheres are joined by a hollow plastic tube that starts at the radius of the small sphere, r = 17.5 cm, and ends at the radius of the large one, R = 38.5 cm. When a charge, q = 6.9 μC, is placed at the inner end of the tube and released from rest, it accelerates straight through the tube and out the other end as shown. - kog ( ² = − 1 / 2 ) kQq R (a) How much did the electric potential energy change as the particle moved from one end of the tube to the other? Write your answer symbolically, in terms of Q, q, r, R and constants (as needed), then calculate its numeric value. AUE= = 8.97 X R x J (b) How much electric potential energy will be left when the little charge is 73.5 cm from the core? UE = 7.48 J 9

Three point charges (Q₁=-5 µC, Q2=-2 µC, and Q3=-5 µC) are on the y-axis at y₁= 8 cm, y₂=0 cm, and y3=-8 cm, respectively. What is the magnitude and direction of the electric field from these charges at point P located on the x-axis at x=6 cm?