A rectangular loop of wire of size 4cm×10cm carries a steady current of 2A. A straight long wire carrying 5A current is kept near the loop, coplanar with it, as shown. 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: (i) Torque =0. (ii) F=1.6×10−5N, directed towards the straight wire (attractive).
Solution
(i) The loop is coplanar with the wire, so the field of the wire lies in the plane of the loop and m (normal to the loop) is perpendicular to B in such a way that the torque τ=m×B on the whole loop is zero (equal and opposite couples cancel). (ii) Only the two sides parallel to the wire contribute a net force, since the field is non-uniform. With the near and far long sides at their respective distances,
F=2×10−7×80=1.6×10−5N,
directed towards the straight wire (the nearer side carries current in the same sense and is attracted more strongly).
