The coil of a generator has a radius of 0.24 m. When this coil is unwound, the wire from which it is made has a length of 5.1 m. The magnetic field of the generator is 0.10 T, and the coil rotates at an angular speed of 35 rad/s. What is the peak emf of this generator? i got 2.63, but my answer is wrong.
10. September 2010 at 8:42 am
V = -dΦ/dt, where Φ is the total flux in webers. 1 tesla = 1 wb/m². For constant field of 0.10 T,
V = -0.10*dA/dt
where A is the normal component of the coil area in the direction of the field
A =π*r²*cps(ω*t)
dA/dT = -ω*π*r²*sin(ω*t)
the peak value of dA/dt is -ω*π*r² (where sin = 1)
so
Vp = 0.10*ω*π*r² per turn of the coil
The number of turns is 5.1/(2*π*r), so total voltage is
Vt = 5.1/(2*π*r)*0.10*ω*π*r² = 0.255*ω*r
Vt = 2.14 v