A magnetic field is perpendicular to the plane of a single-turncircular coil. Th

Question

A magnetic field is perpendicular to the plane of a single-turncircular coil. The magnitude of the field is changing, so that anemf of 0.65 V and a current of3.1 A are induced in the coil. The wire isthe re-formed into a single-turn square coil, which is used in thesame magnetic field (again perpendicular to the plane of the coiland with a magnitude changing at the same rate). What emf andcurrent are induced in the square coil? emf 1 V current 2 A
What formula is needed to solve for each?

Section 22.4 Faraday's Law ofElectromagnetic Induction emf 1 V current 2 A

Explanation / Answer

Induced emf E = A dB / dt
                0.65= A dB / dt Induced current I = E / R from tis resistance R = E / I = 0.65 / 3.1 = 0.2096ohm Side of the square a = A perimeter of square = 4A circumfeence of circle = 4A          2r = 4A    radius r = 0.6366 A Area of circle   A ' = r ^ 2                              = 1.273 A So, Induced emf E ' = A ' dB / dt                                = 1.273 A dB / dt                                = 1.273 * 0.65 = 0.827 V Induced current I ' = E ' / R                              = 3.947 A

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