Question

O spira circulara cu raza r=1cm este asezata perpendicular pe liniile unui camp magnetic care variaza in timp dupa legea B=25/pi sen(200t) (T)
Se se afle:
a) expresia instantanee a fluxului magnetic care strabate spira
b) valoarea instantanee a tensiunii care se stabileste prin spira

Answer 1

$a)r=1 cm=10^{-2} m \\\phi=B*S=B*\pi*r^2=\frac{25}{\pi}sin(200t)*\pi*10^{-2}=2,5*10^{-3}sin(200t) (Wb)=2,5sin(200t)(mWb))=>\omega=200 rad/s;\phi_{m}=2,5 mWb\\\phi=2,5sin(200t)(mWb)$

$b) e=-\frac{\Delta\phi}{\Delta t}=-\omega *\phi_{m}*sin(\omega t+\frac{\pi}{2})\\\omega=200 rad/s;\phi_{m}=2,5 mWb=2,5*10^{-3}Wb\\e=-\omega *\phi_{m}*sin(\omega t+\frac{\pi}{2})=-0,5sin(200t+\frac{\pi}{2})=-0,5cos(200t)(V)=>E_m=0,5 V\\ E=\frac{E_m}{\sqrt2}=\frac{0,5}{\sqrt2}\approx354,6*10^{-3}V=>E=354,6 mV$