Question

A wire 88 cm long is bent into a circular loop and kept with its plane perpendicular to a magnetic field of induction 2.5 Wb/m^2. Within 0.5 second, the coil is changed to a square and the magnetic induction is increased by 0.5 Wb/m^2.. Calculate the emf induced in the wire.

Answer 1

Data: l = 88 cm, 

B = 2.5 Wb/m², 

B = 3 Wb/m², 

∆t = 0.5 s

For the circular loop, l = 2πr

∴ r = \(\cfrac{l}{2\pi}\) = \(\cfrac{88}{2\times(22/7)}\) = 14 cm = 0.14 m

Area of the circular loop, A_i = πr²

= \(\cfrac{22}7\)(0.14)² = 0.0616 m²

Initial magnetic flux, Φ_i = A_iB_i

= 0.0616 × 2.5 = 0.154 Wb 

For the square loop, length of each side

= \(\cfrac{88}4\) cm = 22 cm = 0.22 m⁴

Area of the square loop, A_f = (0.22)²

= 0.0484 m²

∴ Final magnetic flux, Φ_f = A_fB_f

= 0.0484 × 3 = 0.1452 Wb

Induced emf, e = – \(\cfrac{Φ_f−Φ_1}{Δt}\) = \(\cfrac{Φ_1−Φ_f}{Δt}\)

∴ e = \(\cfrac{0.154 - 0.1452}{0.5}\) =8.8 x 10^-3 x 2

= 1.76 × 10^-2 V