A closed coil of wire (N= 50) is attached to an ammeter and inserted in a C- sha

Question

A closed coil of wire (N= 50) is attached to an ammeter and inserted in a C- shaped magnet. Assume the loop axis is aligned with the field. The faces of the C-shaped magnet each measure 3.75 cm in diameter, and the wire loop itself measures 7 cm x 7 cm.

a.) What is the change in magnetic flux for the loop of wire from before it is placed within the permanent magnet’s field to afterward if the magnetic field strength is 0.5 T? Show your work in the space below. SHOW ALL WORK

b.) With what frequency should you insert and remove the 50-turn coil from the magnetic field in order to produce 1-volt of potential difference across the wire? (This voltage will oscillate between +1 V and -1 V) Show your work in the space below. (Hint: Frequency is related to the period of oscillation, where in this case, the period is the time it takes to fully insert AND THEN fully remove the coil from within the field) SHOW ALL WORK

Explanation / Answer

a) change in magnetic flux for the loop of wire = B *A - 0

                                                                          =   0.5 * 50 * (4.9 * 10-3)

                                                                          = 0.1225   webers

b)      emf induced = - (rate of change of magnetic flux)

    =>    1 =   0.1225/T

=>   1 = 0.1225 * f

=> f   = 8.1632 Hz       -----------------------> frequency should you insert and remove

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