An electric field can induce an electric dipole in a neutral molecule (or atom) by pushing the positive and negative charges inside the molecule in opposite directions. the dipole moment of the induced dipole is directly proportional to the electric field at the molecule. that is, p=αe , where p is the induced dipole moment, α is called the polarizability of the molecule, and e⃗ is the electric field at the molecule. a stronger electric field at the molecule results in a more polarized molecule and causes a larger dipole moment p . a molecule with a larger polarizability, α, will be more polarized when subjected to the same electric field. find an expression for the magnitude of the force f⃗ ionondipole. express your answer in terms of the variables q, r, α and appropriate constants.

Aproton is projected toward a fixed nucleus of charge +ze with velocity vo. initially the two particles are very far apart. when the proton is a distance r from the nucleus its velocity has decreased to 1/2vo. how far from the nucleus will the proton be when its velocity has dropped to 1/4vo?

Time remainin52: 42the chart shows data for a moving object.which conclusion is best supported by the information inthe chart? time (s)velocity (m/s

Astudent throws a water balloon with speed v0 from a height h = 1.76 m at an angle θ = 21° above the horizontal toward a target on the ground. the target is located a horizontal distance d = 9.5 m from the student’s feet. assume that the balloon moves without air resistance. use a cartesian coordinate system with the origin at the balloon's initial position. (a) what is the position vector, rtarge t, that originates from the balloon's original position and terminates at the target? put this in terms of h and d, and represent it as a vector using i and j. (b) in terms of the variables in the problem, determine the time, t, after the launch it takes the balloon to reach the target. your answer should not include h. (c) create an expression for the balloon's vertical position as a function of time, y(t), in terms of t, vo, g, and θ. (d) determine the magnitude of the balloon's initial velocity, v0, in meters per second, by eliminating t from the previous two expressions.