1.

A magnetic field B = 2t + 4t^(2) (where t = time) is applied perpendicular to the plane of a circular wire of radius and resistance R. If all the units are in SI the electric charge that flows through the circular wire during t = 0s to t = 2 s is

Answer»

`(6pir^(2))/R`
`(20pir^(2))/R`
`(48pir^(2))/R`
`(20pi r^(3))/R`

Solution :Here, `B = 2t + 4T^(2)`
At t = 0, initial magnetic field `B_(i) = 0T`
At t= 2 s, final magnetic field `B_(f)= 2(2) +4(2)^(2) = 20T`
As `q= (Delta) q = (Delta phi)/R=(pi r^(2)(B_(f)-B_(i)))/R = (pir^(2)(20-0))/R = (20pir^(2))/R`


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