A uniform magnetic field passes through a horizontal circular wire loop at an angle 19.5 ∘ from the vertical. The magnitude of the magnetic field B changes in time according to the equation B ( t ) = ( 3.75 T ) + ( 3.05 T s ) t + ( − 6.95 T s 2 ) t 2 If the radius of the wire loop is 0.220 m , find the magnitude E of the induced emf in the loop when t = 5.71 s .

To solve this problem, we will apply the concepts related to Faraday's law that describes the behavior of the emf induced in the loop. Remember that this can be expressed as the product between the number of loops and the variation of the magnetic flux per unit of time. At the same time the magnetic flux through a loop of cross sectional area is,

Here,

= Angle between areal vector and magnetic field direction.

According to Faraday's law, induced emf in the loop is,

At time ,  Induced emf is,

Therefore the magnitude of the induced emf is 10.9V

an obstruction