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A current carrying rod AB is placed in a uniform magnetic field making and angle $θ$ with the field and the force experienced by the rod is 3N. When the rod is rotated clockwise through an angle of $90^{o}$ in the plane containing the rod and the magnetic field vector $\vec{B},$ force experienced by the rod is 4N. What will be the force experienced by the same rod when it is placed to the same field making an angle of $90^{o}$ with the field ?

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$5 \sqrt{3} N$

$4 \sqrt{3} N$

$3 \sqrt{3} N$

answer is A.

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Detailed Solution

$\begin{array}{l} F_{1} = ilB sinθ and F_{2} = ilB \sin (90^{0} - θ) \\ ∴ F = ilB \sin 90^{0} = ilB \end{array}$

$\begin{array}{l} Now, F_{1}^{2} + F_{2}^{2} = {(ilB)}^{2} (\sin^{2} θ + \cos^{2} θ) = {(ilB)}^{2} = F^{2} \\ ∴ F = \sqrt{F_{1}^{2} + F_{2}^{2}} = \sqrt{3^{2} + 4^{2}} N = 5 N . \end{array}$

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