In a electric fence of length , pulses are used in which a constant high voltage difference V is applied between the wire and ground over a very short period t. Between two pulses there is no voltage difference. (For this issue, we assume that the wire is at a higher voltage than the earth and that the wire is suspended horizontally at a height of 1.00 m). During a pulse, a positive charge also comes onto the fence wire, with a line charge density . This charge generates an electric field pointing from the wire to the earth. We approximate this field with the formula for an infinitely long straight line of charge: E = For this situation, solve the following questions and provide numerical answers with the correct number of significant digits:

(a) Consider a water molecule suspended in air at a distance r_H2O from the wire. Initially, it is facing the wire with its dipole moment. During a pulse, the electric field at the molecule forces a 180 rotation, causing the molecule to suddenly point away from the wire with its dipole moment. What is the labor provided by the electric field (and thus the battery that drives the shock wire) in this process? A water molecule has a dipole moment of p_H2O. You may assume that at the scale of a water molecule, the electric field is nearly homogeneous. (b) How much energy does the battery deliver in a pulse when charging the wire? (The result from the previous step is a small piece of this and you don't need it in the calculation).

=958,8 m t =2,759 ms V =2,58kV

=1,759 C m¹ r_H2O =45,4 cm p_H2O =6,18610³⁰ C m