A wire of length 6 m placed along y-axis is moving with velocity 3 i -4 j-12 k - in a magnetic field- B -7 i -24 j - What will be the emf across the endsof the wire-A- 480 VB- 560 VC- 280 VD- 504 V

The correct option is D 504 VEMF induced =v→×B→.l→v→×B→=i^j^k^34127240=i^( 288) j^( 84)+k^(44)= 288i^+84j^+44k^ v→×B→.l→=( 288i^+84j^+44k^).(6j^)v→×B→.l→=84×6= ...

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Standard XII

Physics

Helical Motion

A wire of len...

Question

A wire of length 6 m placed along y-axis is moving with velocity $3 ˆ i + 4 ˆ j + 12 ˆ k$ in a magnetic field, $\to B = 7 ˆ i + 24 ˆ j$ . What will be the emf across the ends of the wire?

480 V

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560 V

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280 V

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504 V

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Solution

The correct option is D 504 V
EMF induced = $((\to v \times \to B) . \to l ∣ ∣ ∣ \to v \times \to B = ⎛ ⎜ ⎝ \begin{matrix} ˆ i & ˆ j & ˆ k 3 & 4 & 12 7 & 24 & 0 \end{matrix} ∣ ∣ ∣ ∣ ∣ = ˆ i ⎛ ⎜ ⎝ - 288 ⎞ ⎟ ⎠ - ˆ j ⎛ ⎜ ⎝ - 84 ⎞ ⎟ ⎠ + ˆ k ⎛ ⎜ ⎝ 44 ⎞ ⎟ ⎠ = - 288 ˆ i + 84 ˆ j + 44 ˆ k$
$(\to v \times \to B) . \to l = (- 288 ˆ i + 84 ˆ j + 44 ˆ k) . (6 ˆ j) (\to v \times \to B) . \to l = 84 \times 6 = 504 V$

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A wire of length 6 m placed along y-axis is moving with velocity 3ˆi+4ˆj+12ˆk in a magnetic field, →B=7ˆi+24ˆj. What will be the emf across the ends of the wire?

A wire of length 6 m placed along y-axis is moving with velocity $3 ˆ i + 4 ˆ j + 12 ˆ k$ in a magnetic field, $\to B = 7 ˆ i + 24 ˆ j$ . What will be the emf across the ends of the wire?