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A uniform magnetic field B exists in a cylindrical region of radius 10 cm as shown in figure. A uniform wire of length 80 cm and resistance $4.0 Ω$ is bent into a square frame and is placed with one side along a diameter of the cylindrical region. If the magnetic field increases at a constant rate of 0.010 T/s, the current induced in the frame

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$3.9 \times 10^{- 5} A$

$2.1 \times 10^{- 2} A$

$2.6 \times 10^{- 5} A$

$1.5 \times 10^{- 4} A$

answer is A.

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Detailed Solution

emf, $| e | = |\frac{d ϕ}{d t}| = S (d B / d t) = \frac{π r^{2}}{2} (\frac{d B}{d t})$

$\begin{array}{rcl} i & = & \frac{| e |}{R} = \frac{π r^{2}}{2 R} (\frac{d B}{d t}) \\ = & \frac{π {(0.1)}^{2}}{2 \times 4} \times 0.01 \\ = & 3.9 \times 10^{- 5} A \end{array}$

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