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Two circular loops of radii R and r (R >...

Two circular loops of radii R and r (R > > r) have same cenre and carry currents I and i respectively. Find the maximum torque and maximum angular acceleration of smallar loop, if it is free to rotate about y axis where as the bigger loop is fixed. (Neglect the inductance of the system). The mas of the smaller loop is m.

Text Solution

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The magnetic induction due to larger current loop at the centre O is
`B = (mu_(0)I)/(2R)`
The magnetic moment of the smaller loop `= mu = (pi r^(2)) i`
`implie` The maximum torque experienced by the smaller loop
`= tau = mu B = (pi r^(2) i) ((mu_(0) I)/(2R)) = (mu_(0) Iir^(2) pi)/(2R)`
`implies` The maximum angular accleration of the smallar loop
`= alpha = (tau)/(1)`, (moment of inerta `I = mr^(2)//2 :.` rotation is about diameter)
`implies alpha = ((mu Iir^(2))/(2R))/((mr^(2))/(2)) = (mu_(0) Ii)/(mR)`
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