A long straight wire carries a current I_(0), at distance a and b=3a from it there are two other wires, parallel to the former one, which are interconnected by a resistance R(figure).A connector slides without friction along the wires with a constant velocity v.Assuming the resistance of the wires,the connector, the sliding contacts and the self-inductance of the frame to be negligible. The point of application (distance from the long wire) of magnetic force on sliding wire due to the long wire is (2a)/(lnx) from long wire.Then find out value of x.

A long straight wire carries a current I_(0), at distance a and b=3a f

1.	A long straight wire carries a current I_(0), at distance a and b=3a from it there are two other wires, parallel to the former one, which are interconnected by a resistance R(figure).A connector slides without friction along the wires with a constant velocity v.Assuming the resistance of the wires,the connector, the sliding contacts and the self-inductance of the frame to be negligible. The point of application (distance from the long wire) of magnetic force on sliding wire due to the long wire is (2a)/(lnx) from long wire.Then find out value of x.
Answer» Solution :`INT`(Torque of elecentary force)=Torque of net force. `(mu_(0)I_(0))/(2pi)Iint(XDX)/x=F_(0)barx=(mu_(0)I_(0))/(2pi)I ln (b/a) barx RARR barx=(b-a)/(ln(b//a))rArrbarx=(2a)/(ln3) rArr x=3`

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