The figure shows a uniform, 3.0-T magnetic field that isnormal to the plane of a

Question

The figure shows a uniform, 3.0-T magnetic field that isnormal to the plane of a conducting, circular loop with aresistance of 1.5 ohms and a radius of 0.024 m. The magnetic fieldis directed out of the paper as shown. Note: The area of the noncircular portion of the wire is considered negligible compared tothat of the circular loop.
A) What is the magnitude of the average induced emf in theloop if the magnitude of the magnetic field is doubled in 0.4seconds?

B) What is the average current around the loop if themagnitude of the magnetic filed is doubled in 0.4seconds?

Explanation / Answer

                Given that the magnetic field is B1 = 3.0T                 The resistance of the loop is R = 1.5                  The radius of the loop is r = 0.024 m                 The final magnetic field is B2 = 2B1 -----------------------------------------------------------------------           Theinduced emf is || = d /dt                                             =d( B.A) /dt                                             =AdB /dt                                            = A ( B2 - B1) /t                                            = (r2)(2B1- B1)/t                                            =  (r2)(B1)/t                                                           =  ((0.024m)2)(3.0T)/(0.4s)                                            = ----------- V         The current is I = / R                                  =------------ A                                                                      

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