1.

There is one conducting circular loop of radius R, which carries current I. There is another conducting circular loop of radius r placed coaxially at a distance x from it. Here r lt lt R and xgt gt R. Emf induced in the smaller loop when current in the bigger loop is changed at a rate of alpha is.

Answer»

`(mu_(0)alphaR^(2)r^(2))/(2pix^(3))`
`(mu_(0)alphaR^(2)r^(2))/(2X^(3))`
`(2mu_(0)alphaR^(2)r^(2))/(x^(3))`
`(mu_(0)alphaR^(2)r^(2))/(4pix^(3))`

Solution :Magnitude of emf induced can be written as follows:
`epsilon= (dphi)/(dt)`
Emf induced when current is CHANGED can be written as follows:`epsilon= (mu_(0)R^(2)pir^(2))/(2x^(3))(dI)/(dt)`
`epsilon= (mu_(0)R^(2)pir^(2))/(2x^(3)) alpha`
`epsilon= (mu_(0)alphaR^(2)pir^(2))/(2x^(3))`
Hence, option (b) is correct.


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