A circular loop of radius 20 cm and resistance is placed in a time varying magnetic field . At , for the plane of the loop

Question

A circular loop of radius 20 cm and resistance $2 Ω$ is placed in a time varying magnetic field $\vec{B} = (2 t^{2} + 2 t + 3) T$ . At $t = 0$ , for the plane of the loop being perpendicular to the magnetic field and, the induced current in the loop at $t = 3 s$ is $\frac{α}{50} A$ . The value of $α$ is ______. $(Take π = \frac{22}{7})$ [2026]

Smart Achievers · Accepted Answer

(44)

$ϕ = B \cdot π r^{2}$

$ε = \frac{d ϕ}{d t} = π r^{2} \frac{d B}{d t}$

$i = \frac{ε}{R} = \frac{π r^{2}}{R} (\frac{d B}{d t}) = \frac{π}{2} {(\frac{1}{5})}^{2} (4 t + 2)$

$for t = 3$

$i = \frac{11}{7} \times \frac{1}{25} \times 14$

$i = \frac{44}{50}$

Solution

Ans.
(44)

$ϕ = B \cdot π r^{2}$

$ε = \frac{d ϕ}{d t} = π r^{2} \frac{d B}{d t}$

$i = \frac{ε}{R} = \frac{π r^{2}}{R} (\frac{d B}{d t}) = \frac{π}{2} {(\frac{1}{5})}^{2} (4 t + 2)$

$for t = 3$

$i = \frac{11}{7} \times \frac{1}{25} \times 14$

$i = \frac{44}{50}$

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Solution

Q. A circular loop of radius 20 cm and resistance 2 Ω is placed in a time varying magnetic field B→=(2t2+2t+3) T. At t=0, for the plane of the loop being perpendicular to the magnetic field and, the induced current in the loop at t=3 s is α50 A. The value of α is ______. (Take π=227) [2026]

Ans. (44) ϕ=B·πr2 ε=dϕdt=πr2dBdt i=εR=πr2R(dBdt)=π2(15)2(4t+2) for t=3 i=117×125×14 i=4450

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Ans.
(44)

$ϕ = B \cdot π r^{2}$

$ε = \frac{d ϕ}{d t} = π r^{2} \frac{d B}{d t}$

$i = \frac{ε}{R} = \frac{π r^{2}}{R} (\frac{d B}{d t}) = \frac{π}{2} {(\frac{1}{5})}^{2} (4 t + 2)$

$for t = 3$

$i = \frac{11}{7} \times \frac{1}{25} \times 14$

$i = \frac{44}{50}$