First slide

Applications involving charged particles moving in a magnetic field

Question

A coil of 100 turns and area $2 \times 10^{- 2} m^{2}$ is pivoted about a vertical diameter in a uniform magnetic field and carries a current of 5A. When the coil is held with its plane in north-south direction, it experiences a couple of 0.3Nm. When the plane is east-west, the corresponding couple is 0.4Nm, the value of magnetic induction is (neglect earth’s magnetic field)…………T.

Moderate

Solution

$\begin{array}{l} T o r q u e, τ = B A N i s in θ \\ \Rightarrow τ \propto Sin θ \\ Case (i) τ_{1} \propto Sin θ N - S \\ Case (i i) τ_{2} \propto Sin (90^{o} - θ) E - W \\ D i v i d i n g, \frac{τ_{1}}{τ_{2}} = t an θ = \frac{0.3}{0.4} = \frac{3}{4} \\ \Rightarrow Sin θ = \frac{3}{5} & Cos θ = \frac{4}{5} \\ N o w, τ = B A N i Sin θ (C o n s i d e r c a s e (i)) \\ \Rightarrow B = \frac{τ}{A N i Sin θ} = \frac{0.3}{2 \times 10^{- 2} \times 100 \times 5 \times \frac{3}{5}} = 0.05 T \end{array}$

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