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Q.

In the figure shown there exist a uniform time varying magnetic field $B = [(\frac{4 T}{s}) t + 0.3 T]$ in a cylindrical region of radius 4m. An equilateral triangular conducting loop is placed in the magnetic field with its centroid on the axis of the field and its plane perpendicular to the field.

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a

emf induced in the complete $Δ A B C$ is $48 \sqrt{3} V$

b

emf induced in one rod is $16 \sqrt{3} V$

c

emf induced in the complete $Δ A B C$ is 48V

d

emf induced in any one rod is 16V

answer is B, D.

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Detailed Solution

$e_{A B} = \frac{d B}{d t}$ area of $Δ A O B$ , using (EMI)
$= (4) \frac{1}{2} \times (4 \times \frac{\sqrt{3}}{2} \times 2) \times 2 = 16 \sqrt{3} V$
Total emf of loop

$= 3 [(4) \frac{1}{2} \times (4 \times \frac{\sqrt{3}}{2} \times 2) \times 2] = 48 \sqrt{3} V$

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