Question

A conducting circular loop is placed in a uniform magnetic field 0.04T with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at 2mm//sec . The induced emf in the loop when the radius is 2cm is

Answer 1

$\huge\underline{\underline{\bf \orange{Question-}}}$

A conducting circular loop is placed in a uniform magnetic field 0.04T with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at 2mm//sec . The induced emf in the loop when the radius is 2cm is

$\huge\underline{\underline{\bf \orange{Solution-}}}$

$\large\underline{\underline{\sf Given:}}$

• Magnetic Field (B) = 0.04T
• radius of the loop starts shrinking ${\sf \dfrac{dr}{dt}=2mm/s}$
• Radius of loop (r) = 2cm

$\large\underline{\underline{\sf To\:Find:}}$

• Induced emf (e)

❏$\large{\boxed{\bf \blue{e=\dfrac{d\phi}{dt}} }}$

$\implies{\sf e=\dfrac{dBA}{dt} }$

$\implies{\sf e=\dfrac{B×πr^2}{dt} }$

$\implies{\sf e = \dfrac{B×2πr×dr}{dt} }$

$\implies{\sf e = 0.04×3.14×2×10^{-2}×2×2×10^{-3} }$

$\implies{\bf \red{e = 1×10^{-5}v}}$

$\huge\underline{\underline{\bf \orange{Answer-}}}$

Induced emf in the loop is ${\bf \red{1×10^{-5}v}}$