Question

A rectangular loop of wire of size `4 cm xx 10 cm` carries a steady current of 2A. A straight long wire carrying 5 A current is kept near the loop as shown. If the loop and the wire are coplanar, find
(i) the torque acting on the loop and
(ii) the magnitude and direction of the force on the loop due to the current carrying wire.

Answer 1

`(i) |vec(tau)|=|vec(M)xx vec(B)|=MB sin theta`
`implies tau =MB sin 0^(@)`
`implies tau =0`
(ii) Force between two currents
Carrying wires, `F=(mu_(0))/(2 pi).(I_(1)I_(2))/(r ).l`
`therefore` Force on arm `AB, F_(AB)`
`=(mu_(0))/(2 pi)xx(5xx2)/(1xx10^(-2))xx(0.10)`
`F_(AB)=(mu_(0))/(2pi)xx100N` [Attraction towards the wire]
Force on arm `CD, F_(CD) =(mu_(0))/(2pi)xx(5xx2)/(5xx10^(-2))xx(0.10)`
`F_(CD)=(mu_(0))/(2pi)xx20N` [Repulsion away from the wire]
Force on arm BC and AD,
`F_(BC)=F_(AD)=0`
`therefore` Resultant force on loop,
`F=F_(AB)-F_(CD)=(mu_(0))/(2pi)(100-20)`
`implies F=2xx10^(-7)xx80==16xx10^(-6)N`.
[Towards the straight wire i.e., force of attraction].