2005Bb3 The figure above shows two point charges, each of charge −2Q, fixed on the y−axis at y=+a and at y=−a. A third point charge of charge -Q is placed on the x− axis at x=2a. Express all algebraic answers in terms of Q, a, and fundamental constants.
a. Derive an expression for the magnitude of the net force on the charge - Q due to the other two charges, and state its direction.
b. Derive an expression for the magnitude of the net electric field at the origin due to all three charges, and state its direction.
c. Derive an expression for the electrical potential at the origin due to all three charges.
d. On the axes below, sketch a graph of the force F on the - Q charge caused by the other two charges as it is moved along the x -axis from a large positive position to a large negative position. Let the force be positive when it acts to the right and negative when it acts to the left.
