Respuesta :
Answer:
B = 0.223T
Explanation:
step 1:
The equation for induced emf is:
emf = N ΔФ/Δt ..............equ(1)
where N = number of turns of the coil
ΔФ = change in magnetic flux of the coil
Δt = time interval
Magnetic flux is given by
Ф = BA cosθ
where B = magnetic field
A = area
θ = Angle between the normal to the plane of the coil and the magnetic field
Area of teh circular coil is constant and also it is given that the magnetic field is uniform. which implies B and A are constant so that the change in magnetic flux is due to the change in θ only
The equation for ΔΦ = BA(Δcosθ).............equ(2)
since the coil rotates through one fourth revolution the value of θ changes from 0° to 90°
The value of (Δcosθ) is found as
Δcosθ = cos90° - cos0°
=0-1
which is -1
put the above value in equation (2)
ΔΦ = -BA
step 2:
put the above equation in equation (1)
emf = -N (-BA)/Δt
=NBA/Δt
B = (emf)Δt/NA
The area of the circular coil is given by
A = πr²
where r is the radius of the coil
A = π(0.375m)²
A = 0.442m²
substitute 11950v for emf, 4.12 ms for Δt, 500 for N and 0.442m² for A in equation (3) to find the magnetic field B
B = [tex]\frac{(11950)(4.12 X 10^{-3}s ) }{(500)(0.442 m^{2} )}[/tex] = 0.223 T
