Question

The loop is in a magnetic field 0.20 T whose direction is perpendicular to the plane of the loop. At t = 0, the loop has area A = 0.285 square m.Suppose the radius of the elastic loop increases at a constant rate, dr/dt = 3.70 cm/s .A) Determine the emf induced in the loop at t = 0.B)Determine the emf induced in the loop at t = 1.00 s .

Answer 1

Answer

given,

magnetic field = 0.20 T

at t = 0

area of loop = 0.285 m²

dr/dt = 3.70 cm/s

$A = \pi r^2$

$r = \sqrt{\dfrac{A}{\pi}}$

$r = \sqrt{\dfrac{0.285}{\pi}}$

r = 0.301

emf at t = 0

$E = \dfrac{d(BA)}{dt} = \dfrac{d(B\pi r^2)}{dt}$

$E = B(2\pi r)\dfrac{dr}{dt}$

$E = 0.2(2\pi \times 0.301 )\times 0.0370$

E = 14 mV

at t = 1 radius of loop

r = 0.301 + 0.037 x 1

r = 0.338 m

emf at t = 1

$E = \dfrac{d(BA)}{dt} = \dfrac{d(B\pi r^2)}{dt}$

$E = B(2\pi r)\dfrac{dr}{dt}$

$E = 0.2(2\pi \times 0.338 )\times 0.0370$

E =15.71 mV