The figure below shows the magnetic flux through a single loop coil as a functio
ID: 1449509 • Letter: T
Question
The figure below shows the magnetic flux through a single loop coil as a function of time. At what times shown in this plot do the magnetic flux and the induced emf have the greatest magnitude? Is the magnitude of the induced emf in this coil greater near t = 0.4 s or near t = 0.5s? Explain At what times in this plot do you expect the induced emf in the coil to have a maximum magnitude? Estimate the induced emf in the coil at times near t = 0.3 s, t = 0.4 s, and 1= 0.5 s. A solenoid is 1.5 m long and has 470 turns per meter. What is the cross-sectional area of this solenoid if it stores 0.31 J of energy when it carries a current of 12 A?Explanation / Answer
5. flux = 4 Wb cos(wt)
and w = 2pi / T = 2pi / 0.4 = 5pi rad/s
flux = 4 cos(5 pi t )
flux will be maximum when 5 pi t = n pi
where n = 0, 1, ,2 .....
t = n/5 = 0, 0.2, 0.4 , 0.6, .....
induced emf = d(flux) / dt = - 4 x 5pi sin(wt)
e =-20 pi sin( 5 pi t)
it will max when 5 pi t = (n+1) pi/2
n = 0,1 ,2, .....
t = (n + 1) / 10
t = 0.1, 0.3, 0.5 .....
b) at t = 0.5, emd is maximum as calculated above
hence emf will be greater at 0.5 s .
c) induced emf = d(flux) / dt = - 4 x 5pi sin(wt)
e =-20 pi sin( 5 pi t)
it will max when 5 pi t = (n+1) pi/2
n = 0,1 ,2, .....
t = (n + 1) / 10
t = 0.1, 0.3, 0.5 .....
d) e = -20 pi sin(5 pi t)
at t = 0.3
e = -20 pi =62.84 Volr
at t = 0.4
e = 0
at t= 0.5
e = 62.84 volt
6. energy stored = L I^2 /2
and L = u0 N^2 A / L = u0 (n^2) L A
energy store. 0.31 = L x (12^2) / 2
L = 4.31 x 10^-3 H
and L = u0 n^2 L A
4.31 x 10^-3 = (4pi x 10^-7) x (470^2) x 1.5 x A
A = 0.0103 m^2