A rectangular loop \( P Q R S \) made from a uniform wire has lengt...
0A rectangular loop \( P Q R S \) made from a uniform wire has length \( a \), width \( b \) and mass \( m \). It is free to rotate about the \( \operatorname{arm} P Q \), which remains hinged along a horizontal line taken as the \( y \)-axis (see figure). Take the vertically upward direction as the \( z \)-axis. A uniform magnetic field \( \mathbf{B}=(3 \hat{\mathbf{i}}+4 \hat{\mathbf{k}}) B_{0} \) exists in the region. The loop is held in the \( x y \)-plane and a current \( I \) is passed through it. The loop is now released and is found to stay in the horizontal position in equilibrium.
(a) What is the direction of the current \( I \) in \( P Q \) ?
(b) Find the magnetic force on the \( \operatorname{arm} R S \).
\( \mathrm{P} \)
(c) Find the expression for \( I \) in terms of \( B_{0}, a, b \) and \( m \).
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