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 :

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

   [tex]\epsilon = \dfrac{-d\phi}{dt}[/tex]

   [tex]\epsilon = \dfrac{-d}{dt}(0.008 \times cos (377 t))[/tex]

   [tex]\epsilon = 0.008\times 377 sin (377 t))[/tex]

   [tex]\epsilon = 3.016 sin (377 t))[/tex]

c) Current induced in the loop

   resistance = 1 Ω

   [tex]I = \dfrac{\epsilon}{R}[/tex]

   [tex]I = \dfrac{ 3.016 sin (377 t)}{1}[/tex]

   [tex]I = 3.016 sin (377 t)[/tex]

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)

The values of the  given questions are mathematically given as

  • ∅ = 0.008 x cos (377 t)
  • e = 3.016 sin (377 t))
  • I = 3.016 sin (377 t)
  • P = 9.096 sin^2 (377 t)
  • t= 0.0241 sin (377 t)  

What is a magnetic field?

A magnetic field is simply defined as a vector field that gives an insight into the magnetic influence on moving electric charges.

Generally, the equation for the Flux   is mathematically given as

 ∅ = BA cos w t

 ∅ = 0.8 x 0.1² x cos (2π x ν)t

 ∅ = 0.008 x cos (377 t)

Generally, the equation for the Flux   is mathematically given as

Generally, the equation for the emf induced is mathematically given as

[tex]e= \frac{-d\phi}{dt}[/tex]

[tex]e = \dfrac{-d}{dt}(0.008 * cos (377 t))[/tex]

e = 3.016 sin (377 t))

Generally, the equation for the Current induced is mathematically given as

[tex]I = \frac{e}{R}[/tex]

I = 3.016 sin(377 t/1

I = 3.016 sin (377 t)

Generally, the equation for the Power is mathematically given as

P=I^2R

Therefore

 P = (3.016 sin (377 t))^2 (1 Ω)  

 P = 9.096 sin^2 (377 t)

Generally, the torque is mathematically given as

t = 0.1^2 x 0.8 x  3.016 sin (377 t)  

t= 0.0241 sin (377 t)

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