A long straight wire carries a current I. At a distance a and b from it there are two other wires parallel to the first one and interconnected through a resistance R. All the wires are in the same plane. A connector slides without friction on the interconnected wires with a constant velocity v. Neglecting the resistances of connecting wires and sliding contacts, The force required to maintain the velocity of the connector constant is ${\left(\frac{{\mu }_{0}I{\log }_e\frac{b}{a}}{n\pi }\right)}^2\frac{v}{R}\text{.}$ Then find the Value of n.