A copper wire of length $$2$$ m placed perpendicular to the plane of magnetic field B→$$=(2i^+4j^)T$$.If it moves with velocity (4i^+6j^+8k^) $$m/$$$$sec$$. The magnitude of dynamic emf (in$$ $$volt) across its ends is $$__________$$.

Dynamic emf $$ed=l$$→.(B$$→×v→$$)(B$$→×v→$$)=i^j^k^240468=i^(32$$−$$0)−$$j^(16$$−$$0)+k^(12$$−$$16)=32i^$$−$$16j^$$−$$4k^$$,$$ed=(2k^)$$⋅$$(32i^$$−$$16j^$$−$$4k^)=$$−$$8$$ volt

Magnetic flux and induced emf

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A copper wire of length 2 m placed perpendicular to the plane of magnetic field $\vec{B} = (2 \hat{i} + 4 \hat{j})$ T.If it moves with velocity $(4 \hat{i} + 6 \hat{j} + 8 \hat{k})$ m/sec. The magnitude of dynamic emf (in volt) across its ends is __________.

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Solution

$\begin{array}{l} Dynamic emf e_{d} = \vec{l} . (\vec{B} \times \vec{v}) \\ \begin{matrix} (\vec{B} \times \vec{v}) = |\begin{array}{ll} \hat{i} & \hat{j} & \hat{k} \\ 2 & 4 & 0 \\ 4 & 6 & 8 \end{array}| \\ = \hat{i} (32 - 0) - \hat{j} (16 - 0) + \hat{k} (12 - 16) = 32 \hat{i} - 16 \hat{j} - 4 \hat{k}, \\ e_{d} = (2 \hat{k}) \cdot (32 \hat{i} - 16 \hat{j} - 4 \hat{k}) = - 8 volt \end{matrix} \end{array}$

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Magnetic flux and induced emf

Remember concepts with our Masterclasses.

A copper wire of length 2 m placed perpendicular to the plane of magnetic field B→=(2i^+4j^)T.If it moves with velocity (4i^+6j^+8k^) m/sec. The magnitude of dynamic emf (in volt) across its ends is __________.

Dynamic emf ed=l→.(B→×v→)(B→×v→)=i^j^k^240468=i^(32−0)−j^(16−0)+k^(12−16)=32i^−16j^−4k^,ed=(2k^)⋅(32i^−16j^−4k^)=−8 volt

Ready to Test Your Skills?

free study material

A copper wire of length 2 m placed perpendicular to the plane of magnetic field $\vec{B} = (2 \hat{i} + 4 \hat{j})$ T.If it moves with velocity $(4 \hat{i} + 6 \hat{j} + 8 \hat{k})$ m/sec. The magnitude of dynamic emf (in volt) across its ends is __________.