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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