1.

A conducting ring of radius r is placed in a varying magnetic field perpendicular to the plane of the ring. If the rate at which the magnetic field varies is x, the electric field intensity at any point of the ring is

Answer»

RX
`(rx)/(2)`
`2rx`
`(4r)/(x)`

Solution :Let `vecE` be the electric field intensity at a point on the circumference of the ring . Then , the emf induced `epsi = OINT vecE.VEC(dl)`where `vec(dl)` is a length ELEMENT of the ring . Since `|vecE|` is constantand `vecE||vec(dl)`
`therefore epsi = E(2pi r)`.....(i)
Also , the induced emf is
`epsi = (dphi)/(dt) = pi r^2 (dB)/(dt) = pi r^2 x `......(ii)
Equating (i) and (ii) , we get`E = (rx)/(2)`


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