Question

A conducting circular loop is placed in a uniform magnetic field 0.02 T with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at 2 mm/s. The induced e.m.f. in the loop when the radius is 2 cm will be ____________.

Options

• `3.8  pi mu  "V"`

• `4.8  pi mu  "v"`

• `0.8  pi mu  "V"`

• `1.6  pi mu  "V"`

Answer 1

A conducting circular loop is placed in a uniform magnetic field 0.02 T with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at 2 mm/s. The induced e.m.f. in the loop when the radius is 2 cm will be `1.6  pi mu  "V"`.

Explanation:

`abs"e" = ("d"phi)/"dt" = "B"("dA")/"dt" = "B""d"/"dt"(pi"r"^2) = 2pi"Br" ("dr")/"dt"`

`therefore abs"e" = 2pi xx 0.02 xx 2 xx 10^-2 xx 2 xx 10^-3`

`= 1.6  pi mu  "V"`