Rotating Rod In Magnetic Field

Consider a horizontal circular loop of radius rr carrying a current II. Concentric and coplanar with the loop is a smooth metallic ring of radius aa, containing a metallic rod OAOA of mass mm, as shown. The rod can freely rotate about OO, the center of arrangement. Between OO and the circumference of ring, a resistor load RR(not shown in the figure) is connected, which doesn't obstruct the motion of rod. The rod is given an angular velocity ω0\omega_{0}. Find an expression for the maximum angle θ\theta through which the rod rotates, if a<<ra<<r.

Find the value of 2(θ163Rmω0(rμ0Ia)2)\displaystyle 2 \Bigg|\bigg(\theta - \frac{16}{3} R m \omega_{0} \bigg(\frac{r}{\mu_{0} I a} \bigg)^2\bigg)\Bigg| for the values given below :

Details and assumptions
The resistances of the rod and ring can be neglected.
m=1g m = 1g
R=1Ω R = 1 \Omega
ω0=1rad/s \omega_{0} = 1 rad/s
r=1m r = 1m
a=1cm a = 1cm
I=1000A I = 1000 A
μ0=4π×107H/m \mu_{0} = 4 \pi \times 10^{-7} H/m


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