A certain elastic conducting material is stretched into a circular loop. It is placed with its plane perpendicular to a uniform magnetic field B =0.8 T. When released the radius of the loop starts shrinking at a constant rate of 2 cm -1. The induced emf in the loop at an instant when the radius of the loop is 10 cm will be mV.

Question

A certain elastic conducting material is stretched into a circular loop. It is placed with its plane perpendicular to a uniform magnetic field B =0.8 T. When released the radius of the loop starts shrinking at a constant rate of 2 cm -1. The induced emf in the loop at an instant when the radius of the loop is 10 cm will be mV. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

text EMF =( d / dt )( B π r 2) =2 B π r ( dr / dt )=2 × π × 0.1 × 0.8 × 2 × 10-2 =2 π × 1.6= 1 0 . 0 6 text [round off 1 0 . 0 6 = 1 0 text ]

EMF =dtd​(Bπr2) =2Bπrdtdr​=2×π×0.1×0.8×2×10−2 =2π×1.6=10.06 [round off 10.06=10 ]

$EMF = \frac{d}{d t} (B π r^{2})$
$= 2 B π r \frac{d r}{d t} = 2 \times π \times 0.1 \times 0.8 \times 2 \times 1 0^{- 2}$
$= 2 π \times 1.6 = 10.06 [round off 10.06 = 10]$