A copper wire with cross-sectional area `S = 2.5 mm^(2)` bent to make three sides of a square can turn about a horizontal axis `OO'` (Fig). The wire is located in unifrom vertical magnetic field. Find the magnetic induction if on passing a current `I = 16 A` through the wire the latter deflects by an angle `theta = 20^(@)`.

Explanation

The Ampere forces on the sides `OP` and `O' P'` are directed along the same line, in opposite directions and have equal values, hence the net force as well as the net torque of these forces about the axis `OO'` is zero. The Ampere-force on the segment `PP'` and the corresponding moment of this force about the axis `OO'` is effective and is deflecting is nature.
In equilibrium (in the dotted position) the deflecting torque must be equal to the restoring torque, develop due to the weight of the shape.
Let, the length of each side be `l` and `rho` be the density of the materail then,
`ilB (l cos theta) = (S l rho) "g" (1)/(2) sin theta + (S l rho) "g" (1)/(2) sin theta + (S l rho) gl sin theta`
or, `il^(2) B cos theta = 2.S rho gl^(2) sin theta`
Hence, `B = (2S rho g)/(i) tan theta`