87. Review. An electric dipole in a uniform horizontal electric field is displaced slightly from ts equilibrium position as shown in Figure P23.87, where θ is small The separation of the charges is 2a, and each of the two particles has mass m. (a) Assuming the dipole is released from this position, show that its angular ori entation exhibits simple harmonic motion with a frequency What If (b) Suppose the masses of the two charged particles in the dipole are not the same even though each particle continues to have charge q. Let the masses of the particles be m and m2. Show that the fre quency of the oscillation in this case is E mm 2amm2 Figure P23.87

2. Charged particle interactions and energy conservation A stationary charge, Q = + 31.0uC, remains fixed in position. A moving charge, q = + 7.70µC, with mass, m = 1.18 x 10 kg, heads toward this stationary charge along the x axis. The moving charge starts at position A with an initial speed of 892 m/s. Point A is 1.64 m from the fixed charge. Point B is 0.550 m from the fixed charge. a. Use energy conservation principles to set up an energy conservation equation for this system. b. Solve the energy conservation equation for the speed of the moving charge, vx, when it reaches point B. q. m >+ x axis Fixed stationary charge

One end of a light spring with force constant k = 125 N/m is attached to a wall, and the other end to a metal block with charge A 1.94 μC on a horizontal, frictionless table as shown in the figure. A second block with charge qB -3.52 μC is brought close to the first block. The spring stretches as the blocks attract each other so that at equilibrium, the blocks are separated by a distance d = 12.8 cm. What is the displacement x of the spring? Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. m ¦ 9A 6000000000000000 + 9A ¨¨¨¨¨¨¨¨ + |←x → ←——_—_d- == 9B

A parallel plate capacitor with a charge of +/-177nC has square plates length L=20.0cm across on each side. The plates are separated by a distance d=10.0cm. A positive +4.0microC point charge is held in place halfway between each plate on the right-most edge of the capacitor. While solving this problem ignore any distortion of the capacitor's electric field along its edges. A) What is the magnitude and direction of the capacitor's electric field at point P, which is midway between the plates and on the left-most edge of the capacitor B) What is the magnitude and direction of the electric field due to the +4.0 microC point charge at point P. C) What is the magnitude and direction of the net electric field at point P