A mysterious force has been discovered in nature that acts on all particles in the three-dimensional space. You determine that the force is always pointed away from a definite point in space, which we can call the force center. The magnitude of the force has the following functionality: F = Ae-br, where r is the distance from the force center to any other point. (the -br is an exponent)

Required:
Write an expression for the potential energy UD of a particle when it is at a distance D from the force center, assuming the potential energy to be zero when the particle is at infinity.

To understand the behavior of the electric field at the surface of a conductor, and its relationship to surface charge on the conductor. a conductor is placed in an external electrostatic field. the external field is uniform before the conductor is placed within it. the conductor is completely isolated from any source of current or charge. part a: which of the following describes the electric field inside this conductor? it is in the same direction as the original external field.it is in the opposite direction from that of the original external field.it has a direction determined entirely by the charge on its surface.it is always zero. part b: the charge density inside the conductor is: 0non-zero; but uniformnon-zero; non-uniforminfinite part c: assume that at some point just outside the surface of the conductor, the electric field has magnitude e and is directed toward the surface of the conductor. what is the charge density η on the surface of the conductor at that point? express your answer in terms of e and ϵ0