A circular coil of radius 8.0 cm and 20 turns is rotated about its vertical diameter with an angular speed of 50 rad `s^(-1)` in a uniform horizontal magnetic field of magnitude `3.0 xx 10^(-2)` T. Obtain the maximum and average emf induced in the coil. If the coil forms a closed loop of resistance 10`Omega`, calculate the maximum value of current in the coil. Calculate the average power loss due to Joule heating. Where does this power come from ?

Explanation

Let bead move on circular path of radius R with angular velocity `epsilon `
Let N be normal reaction
At any instant position of bead be A
Direction of normal force is toward direction AO Two component of N are N cos `theta` and N sin `theta `

Consider equilibrium of bead at point A
N cos `theta` =mg
N sin `theta = m R epsilon ^(2) sin epsilon`
m R `epsilon^(2) sin theta` is horizontal component of centripetal force
N cos `theta` = mg
cos `theta = ( g)/( R epsilon^(2))`
When bead is at lowermost position `theta= 0 ^ (@)`
`g= R epsiloon ^(2)`
`epsilon= sqrt((g )/( R ))`
If `=sqrt((2 g)/( R ))` then from equation (4 )
`cos theta = (g )/( R epsilon ^(2)) = (g ) /(R ) xx (R ) /(2G)`
`cos theta = (1)/( 2)`
`theta = 60^(@)`