A resitance `R=1kOmega` connected to a conducting rod `PQ` that can slide on a conducting circular ring of radius `2m` with center at `P`. A constant uniform magnetic field 10 Tesla exist as shown in figure. At `t=0`, switch `'S'` is closed and simulaneously an external torque is applied on the rod so that it rotates with constant angular velocity `20"rad"//"sec"`. The magnitude of power delivered by external is `20K` Watt. Find the value of `K`. (Neglect the gravity, friction and self inductance of circular loop)

Answer

8

Explanation

Induced emf `=(Bomegal^(2))/2`, current `i_(0)=(Bomegal^(2))/(2R)`
Torque about `P=tau=int(idx)B.x=(iBl^(2))/2`
`=((Bomegal^(2))/(2R))((Bl^(2))/2)=8`
So, power `P= tau.vecomega=160` Watt
Alternate Solution
Power `=` Heat loss in resistance `=Ri_(1)^(2)=(B^(2)omega^(2)l^(4))/(4R)=160` Watt