Near Mid-Night question of the day [6]
A wire shpaed as a semi circle of radius a rotates about axis OO' with an angular velocity ω in a uniform magnetic field of induction B. The rotation axis is perpendicular to the field direction. The total resistance of the circuit is equal to R. Neglecting the magnetic field of the induced current, find the mean amount of thermal power being generated in the loop during a rotation period.
Image in the following post...
**** Edit****
Another one Shamelessly lifted from IE Irodov ;)
*** End Edit ***
1in time t the angle between the B and area= θ
Einduced= -d(φb)/dt=-Bd(Acoswt)/dt=BAwsinwt=E0sinwt
so thermal power= 0∫2π/wE0sinwt*idt
but i= E0sinwt/R
so total thermal power(after calculating )= (E02/2R )T
hence mean thermal power = E02/2R
sry forgot to mention E0=BÏ€a2w/2
