(Solved): A rectangular coil has 16 turns and sides of length \( \mathrm{a}=15 \mathrm{~cm} \) and \( \mathr ...

A rectangular coil has 16 turns and sides of length \( \mathrm{a}=15 \mathrm{~cm} \) and \( \mathrm{c}=40 \mathrm{~cm} \). The coil is pivoted about the \( \mathrm{z} \) axis and its plane is at \( \theta=29^{\circ} \) to a magnetic field \( \mathbf{B}=0.2 \mathbf{i T} \), as shown in the figure above. If \( \mathrm{I}=8 \mathrm{~A} \), find: a) the force on each side. \[ \begin{array}{l} \mathbf{F}_{1}=(\quad \mathbf{i}+\mathbf{j}+\mathbf{k}) \mathrm{N} \\ \mathbf{F}_{2}=(\square \mathbf{i}+\square \mathbf{j}+\square \mathbf{k}) \mathrm{N} \\ \mathbf{F}_{3}=(\quad \mathbf{i}+\mathbf{j}+\mathbf{k}) \mathrm{N} \\ \mathbf{F}_{4}=(\quad \mathbf{i}+\mathbf{j}+\quad \mathbf{k}) \mathrm{N} \\ \end{array} \] b) What is the magnetic moment of the coil? \[ \boldsymbol{\mu}=(\quad \mathbf{i}+\mathbf{j}+\quad \mathbf{k}) \mathrm{A} \cdot \mathrm{m}^{2} \] c) What is the torque on the coil? \( \boldsymbol{\tau}=(\quad \mathbf{i}+\quad \mathbf{j}+\quad \mathbf{k}) \mathrm{N} \cdot \mathrm{m} \)