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Magnetic Flux and Faraday's Law

If area vecto...

Question

If area vector $\to A = 3^i + 2^j + 5^k m^{2}$ flux density vector $\to B = 5^i + 10^j + 6^k (W b / m^{2})$ . The magnetic flux linked with the coil is

A

31 W b

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B

9000 W b

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C

65 W b

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D

100 W b

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Solution

The correct option is D $65 W b$
$ϕ_{B} = \to B . \to A$
$= (5^i + 10^j + 6^i) . (3^j + 2^j + 5^k)$
$= 15 + 20 + 30$
$= 65 W b$

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