A wire is bent in the form of a parabola y=x2. A cell is connected to the wire across the points (0,0) and (1,1) due to which a current 1A flows. If a magnetic field B→=i^+3j^+2k^ exists in the space then find magnetic force on the wire. [take all quantities in SI units] (Take 3=1.73)

l→=i^+j^ ∴F→=i(l→×b→)=|i^j^k^110132|=2i^−2j^+2k^ ∴F=23=3.46

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A wire is bent in the form of a parabola $y = x^{2}$ . A cell is connected to the wire across the points (0,0) and (1,1) due to which a current 1A flows. If a magnetic field $\vec{B} = \hat{i} + 3 \hat{j} + 2 \hat{k}$ exists in the space then find magnetic force on the wire. [take all quantities in SI units] (Take $\sqrt{3} = 1.73$ )

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answer is 3.46.

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Detailed Solution

$\vec{l} = \hat{i} + \hat{j} ∴ \vec{F} = i (\vec{l} \times \vec{b}) = | \begin{matrix} \hat{i} & \hat{j} & \hat{k} \\ 1 & 1 & 0 \\ 1 & 3 & 2 \end{matrix} | = 2 \hat{i} - 2 \hat{j} + 2 \hat{k} ∴ F = 2 \sqrt{3} = 3.46$

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