Question

A magnetic field is perpendicular to the plane of a single-turn circular coil. The magnitude of the field is changing, so that an emf of 0.25 V and a current of 2.5 A are induced in the coil. The wire is then re-formed into a single-turn square coil, which is used in the same magnetic field (again perpendicular to the plane of the coil and with a magnitude changing at the same rate). What (a) emf and (b) current are induced in the square coil?

Answer 1

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we know

E = d / dt

E = BdA/ dt

note that only area is changing, rest everything is same

so, we can compare the area of given loops

E ( square) / E (circle) = A (square) / A (circle)

we need to find side of square

there are four sides, and total length of wire is same as circumference of circle = 2r

so,

4d = 2r

d = r / 2

so,

area of square = ²r² / 4

so,

now

E ( square) / E (circle) = ²r² / 4 / r²

E ( square) / E (circle) = / 4

E ( square) =   / 4 * E (circle)

E ( square) =   / 4 * 0.25

E ( square) = 0.196 V

and

I (square) = I (circle) * E ( square) / E (circle)

I (square) = 2.5 * 0.196 / 0.25

I (square) = 1.96 A