Radius of a circular loop placed in a perpendicular uniform magnetic field is increasing at a constant rate of r0 ms -1. If at any instant radius of the loop is r, then emf induced in the loop at that instant will be

Question

Radius of a circular loop placed in a perpendicular uniform magnetic field is increasing at a constant rate of r0 ms -1. If at any instant radius of the loop is r, then emf induced in the loop at that instant will be (A) -2 B rr0 (B) -2 B π r (C) -B π r0 r (D) -2 B π r0 r

Tardigrade Admin · Accepted Answer

(d r/d t)=r0 ⇒ φ=B π r2 ε=(-d φ/d t)=-B π(2 r) (d r/d t) ε=-2 π B r0

Q. Radius of a circular loop placed in a perpendicular uniform magnetic field is increasing at a constant rate of $r_{0} m s^{- 1}$ . If at any instant radius of the loop is $r$ , then emf induced in the loop at that instant will be

$- 2 B r r_{0}$

$- 2 B π r$

$- B π r_{0} r$

$- 2 B π r_{0} r$

$\frac{d r}{d t} = r_{0}$
$\Rightarrow ϕ = B π r^{2}$
$ε = \frac{- d ϕ}{d t} = - B π (2 r) \frac{d r}{d t}$
$ε = - 2 π B r_{0}$

Q. Radius of a circular loop placed in a perpendicular uniform magnetic field is increasing at a constant rate of r0​ms−1. If at any instant radius of the loop is r, then emf induced in the loop at that instant will be

−2Brr0​

−2Bπr

−Bπr0​r

−2Bπr0​r