A conducting loop of area 5.0 cm ^2 is placed in a magnetic field which varies sinusoidally with time as B = B₀ t where B₀ = 0.20 T and = 300 s ⁻¹ . The normal to the coil makes an angle of 60^ with the field. Determine the emf induced at t = ( 900 ) s .

Step-by-step solution

The magnetic flux linked with the conducting loop is given by = B A Substituting B = B₀ t , we get = B₀ A t By Faraday's law of electromagnetic induction, the magnitude of the induced emf is |e| = | d dt | = B₀ A t Given values are: B₀ = 0.20 T A = 5.0 cm ^2 = 5.0 10⁻⁴ m ^2 = 300 s ⁻¹ = 60^ t = 900 s Calculating the phase angle t : t = 300 900 = 3 rad = 60^ Substituting the values into the emf equation: |e| = (0.20) (5.0 10⁻⁴) (300) 60^ 60^ |e| = 0.20 5.0 10⁻⁴ 300 1 2 1 2 |e| = 1.0 10⁻⁴ 300 0.25 |e| = 75 10⁻⁴ V = 7