Chapter 28, Problem 28.79CP

CP Two long, straight conducting wires with linear mass density λ are suspended from cords so that they are each horizontal, parallel to each other, and a distance d apart. The back ends of the wires are connected to each other by a slack, low-resistance connecting wire. A charged capacitor (capacitance C) is now added to the system; the positive plate of the capacitor (initial charge +Qo) is connected to the front end of one of the wires, and the negative plate of the capacitor (initial charge −Q₀) is connected to the front end of the other wire (Fig. P28.79). Both of these connections are also made by slack, low-resistance wires. When the connection is made, the wires are pushed aside by the repulsive force between the wires, and each wire has an initial horizontal velocity of magnitude v_o. Assume that the time constant for the capacitor to discharge is negligible compared to the time it takes for any appreciable displacement in the position of the wires to occur, (a) Show that the initial speed ʋ_Q of either wire is given by

${\upsilon }_0\text{ = }\frac{{\mu }_0{\text{Q}}_0^2}{4\pi \lambda \text{RCd}}$

where R is the total resistance of the circuit, (b) To what height h will each wire rise as a result of the circuit connection?

Figure P28.79