A negatively charged particle with q = -1 uC is placed at the center of the uniformly charged cube with side a=1 mm and total charge Q = 3 C spread out over all six faces of the cube. What is the total force acting on the particle in the center? Find the magnitude and the direction.

Two thin uniformly charged rods, each with length L and total charge +Q, are parallel and separated by a distance a. The first rod has one end at the origin and its other end on the positive y-axis. The second rod has its lower end on the positive x-axis. Determine the x-component of the differential force dF2 exerted on a small portion of the second rod, with length dy2 and position y2, by the first rod. (This requires integrating over differential portions of the first rod, parameterized by dy1.) Express your answer in terms of some or all of variables Q, L, y2, dy2, a, and the electric constant ϵ0.

Two small beads having positive charges q1 = 29q and q2 = q are fixed at the opposite ends of a horizontal insulating rod of length d = 1.50 m. The bead with charge q1 is at the origin. As shown in the figure below, a third small, charged bead is free to slide on the rod.   (a) At what position x is the third bead in equilibrium?x =  m(b) Can the equilibrium be stable?

Three charged particles form an equilateral triangle with side length d = 1.0 cm.   The values of the charges are: 91 = +1.0 uC 92 = +1.0 MC 93 = -4.0 MC What is the magnitude of the net force acting on 93? Express your answer to the nearest N.

Four point charges are located at the corners of a square. Each charge has magnitude 3.10 nC and the square has sides of length 2.50 cm. Find the magnitude of the electric field (in N/C) at the center of the square if all of the charges are positive and three of the charges are positive and one is negative. (a)all the charges are positive   (b)three of the charges are positive and one is negative

A positively charged particle Q1 = +25 nC is held fixed at the origin. A second charge Q2 of mass m = 9.5 μg is floating a distance d = 45 cm above charge Q1. The net force on Q2 is equal to zero. You may assume this system is close to the surface of the Earth.  Calculate the magnitude of Q2 in units of nanocoulombs.

In the figure three charged particles lie on an x axis. Particles 1 and 2 are fixed in place. Particle 3 is free to move, but the net electrostatic force on it from particles 1 and 2 happens to be zero. If L23 = L12, what is the ratio q1/q2? L23 '12 3 1