Dipole moment of coil is $2^i + 3^j + 4^k$ . If this coil is placed in unifrom magnetic field having magnitude $5^k T$ , toque acting on it is______________ $N m$ .

\sqrt{125}

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\sqrt{225}

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\sqrt{325}

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\sqrt{425}

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Solution

The correct option is C $\sqrt{325}$
$G i v e n :$ $\to M$ = $2$ $^ı$ + $3$ $^ȷ$ + $4$ $^k$
$\to B$ = $5$ $K$ $T$
$S o l u t i o n :$ Torque on the dipole moment is
$\to T$ = $\to M$ $\times$ $\to B$
$\to T$ = ( $2$ $^ı$ + $3$ $^ȷ$ + $4$ $^k$ ) $\times$ ( $5$ $^k$ )
$\to T$ = $10$ ( $-^ȷ$ ) + $15$ ( $-^ı$ ) + $20$ $\times$ $(0)$
$\to T$ = $10$ ( $-^ȷ$ ) + $15$ ( $-^ı$ )
Magnitude of torque

$|$ $\to T$ $|$ = $\sqrt{10^{2} + 15^{2}}$ = $\sqrt{100 + 225}$ = $\sqrt{325}$ $N M$
$S o, t h e$ $c o r r e c t$ $o p t i o n : C$

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Dipole moment of coil is 2^i+3^j+4^k. If this coil is placed in unifrom magnetic field having magnitude 5^k T, toque acting on it is______________Nm.

Dipole moment of coil is $2^i + 3^j + 4^k$ . If this coil is placed in unifrom magnetic field having magnitude $5^k T$ , toque acting on it is______________ $N m$ .