A rectangular loop of wire of size 4 cm `xx` 10 cm carries a steady current of 2A. A straight long wire carrying 5A current is kept near the loop (fig). 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.

Explanation

(i) From the symmetry of the fig it is clear that forces actig on parts BC and AD of rectangular current loop are exactly equal, oppisite and collinear. Again forces acting on parts AB and CD are mutually opposite, collinear but of different magnitudes. Hence, net torque acting on the loop is zero.
(ii) Here `I_1 = 5 A, I_2 = 2 A, l = 10 cm = 0.10 m, b = 4 cm = 0.04 m` Distance of AB from current carrying straight wire `r_1 = 1 cm = 0.01 m`
`:.` Force on `AB, F_1 = (mu_0 I_1 I_2 l)/(2 pi r_1) = (4 pi xx 10^(-7) xx 5 xx 2 xx 0.1)/(2 pi xx 0.01)`
`= 2 xx 10^(-5)` Nand the force is attractive in nature.
Distance of CD from current carrying straight wire
`r_2 = r_1 + b = (1 + 4) cm = 5 cm = 0.05 m`
`:.` Force on CD, `F_2 = (mu_0 I_1 I_2 l)/(2 pi r_2) = (4 pi xx 10^(-7) xx 5 xx 2 xx 0.1)/(2 pi xx 0.05)`
`= 4 xx 10^(-6)` Nand the force is repulsive in nature,
`:.` Net force one the loop `F = F_1 - F_2 = (2 xx 10^(-5) - 4 xx 10^(-6))N`
`= 1.6 xx 10^(-5) N` (attractive)