A graph of the induced EMF versus time for a coil rotating in a uniform magnetic field is a sinusoidal curve. From the graph, the peak-to-peak EMF is read as 628 V and the time for one complete cycle is 0.02 s . If the coil consists of 500 turns and has a cross-sectional area of 0.1 m ^2 , what is the magnitude of the uniform magnetic field? (Take = 3.14 )

Step-by-step solution

From the described graph, the peak-to-peak EMF is 628 V . The peak (maximum) induced EMF is half of this value: E_ max = 628 2 = 314 V The time period T = 0.02 s . The angular velocity is: = 2 T = 2 3.14 0.02 = 314 rad s ⁻¹ The maximum induced EMF for a rotating coil is given by: E_ max = NAB Substituting the given values ( N = 500 , A = 0.1 m ^2 ): 314 = 500 0.1 B 314 1 = 50 B B = 1 50 = 0.02 T Using the peak-to-peak value directly instead of the peak value leads to 0.04 T , while confusing angular velocity with f