Question

The rotating loop in an AC generator is a square 10.0 cm on each side. It is rotated at 60.0 Hz in a uniform magnetic field of 0.800 T. Calculate
(a) the flux through the loop as a function of time,
(b) the emf induced in the loop,
(c) the current induced in the loop for a loop resistance of 1.00 V,
(d) the power delivered to the loop, and
(e) the torque that must be exerted to rotate the loop.

Answer 1

Answer

given,

Side of rotating loop is square = 10 cm

frequency of the rod(ν) = 60 Hz

magnetic field of the loop (B)= 0.8 T

a) Flux through the loop is calculated by

  ∅ = BA cos ω t

  ∅ = 0.8 x 0.1² x cos (2π x ν)t

  ∅ = 0.8 x 0.1² x cos (2π x 60)t

  ∅ = 0.008 x cos (377 t)

b) emf induced in the loop

   $\epsilon = \dfrac{-d\phi}{dt}$

   $\epsilon = \dfrac{-d}{dt}(0.008 \times cos (377 t))$

   $\epsilon = 0.008\times 377 sin (377 t))$

   $\epsilon = 3.016 sin (377 t))$

c) Current induced in the loop

   resistance = 1 Ω

   $I = \dfrac{\epsilon}{R}$

   $I = \dfrac{ 3.016 sin (377 t)}{1}$

   $I = 3.016 sin (377 t)$

d) Power delivered to the loop

   P = I² R

   P = (3.016 sin (377 t))² (1 Ω)

   P = 9.096 sin² (377 t)

e) torque required to rotate loop

   τ = A B I

   τ = 0.1² x 0.8 x  3.016 sin (377 t)

   τ = 0.0241 sin (377 t)