A rectangular loop PQRS made from a uniform wire has length \( a \)...
0A rectangular loop PQRS made from a uniform wire has length \( a \), width \( \mathrm{b} \) and mass \( \mathrm{m} \). It is free to rotate about the arm PQ, 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 \( \overrightarrow{\mathrm{B}}=(3 \hat{\mathrm{i}}+4 \hat{\mathrm{k}}) \mathrm{B}_{0} \) exists in the region. The loop is held in the \( x-y \) plane and a current \( \mathrm{I} \) 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 PQ?
(b) Find the magnetic force on the arm RS.
(c) Find the expression for \( \mathrm{I} \) in terms of \( \mathrm{B}_{0}, \mathrm{a}, \mathrm{b} \) and \( \mathrm{m} \).
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