A small object with electric dipole moment p is placed in a non-uniform electric field E = E(x)i. That is, the field is in the x direction and its magnitude depends on the coordinate
x. Let θ represent the angle between the dipole moment and the x direction. (a) Prove that the dipole feels a net force in the direction toward which the field increases.
(b) Consider a spherical balloon centered at the origin, with radius 15.0 cm and carrying charge 2.00 μC. Evaluate dE/dx at the point (16 cm, 0, 0). Assume a water droplet at this point has an induced dipole moment of 6.30ˆi nC+m. Find the force on it.