Respuesta :
Answer:
The magnetic field strength needed is 1.619 T
Explanation:
Given;
Number of turns, N = 485-turn
Radius of coil, r = 0.130 m
time of revolution, t = 4.17 ms = 0.00417 s
average induced emf, V = 10,000 V.
Average induced emf is given as;
V = -ΔФ/Δt
where;
ΔФ is change in flux
Δt is change in time
ΔФ [tex]= -NBA(Cos \theta_f - Cos \theta_i)[/tex]
where;
N is the number of turns
B is the magnetic field strength
A is the area of the coil = πr²
θ is the angle of inclination of the coil and the magnetic field,
[tex]\theta_f = 90^o\\\theta_i = 0^o[/tex]
V = NBACos0/t
V = NBA/t
B = (Vt)/NA
B = (10,000 x 0.00417) / (485 x π x 0.13²)
B =1.619 T
Thus, the magnetic field strength needed is 1.619 T
Answer:
B = 1.619 T
Explanation:
We are given;
Radius of coil, r = 0.13 m
Number of turns; N = 485-turn
Time of revolution, t = 4.17 ms = 0.00417 s
Average induced emf = 10,000
The equation for the for the induced emf is given by;
EMF = -N(ΔФ/Δt)
where;
N is number of turns of coil
ΔФ is change in magnetic flux
Δt is change in time interval
The change in magnetic flux is given by the formula ;
ΔФ = BAcosθ
where;
B is the magnetic field strength
A is the area of the coil = πr²
θ is the angle between the normal to the plane and the magnetic field,
Now, since the coil rotates through one fourth of a revolution, the value of θ changes from 0° to 90°
The value of Δcosθ is found as;
Δcosθ = cos90 - cos0 = 0 - 1 = - 1
Thus,
ΔФ = BAcosθ = -BA
And so, EMF = -N(-BA/Δt) = NBA/Δt
Making B the subject, we have;
B = ((EMF)Δt)/NA
A = πr² = π x 0.13² = 0.0531 m²
Thus, B = ((10000•0.00417)/(485•0.0531) = 1.619 T
V = NBA/t
B = (Vt)/NA
B = (10,000 x 0.00417) / (485 x π x 0.13²)
B =1.619 T
Thus, the magnetic field strength needed is 1.619 T
