A conducting loop (in the shape of a rectangle) and with aresistance of 5 ohms m

Question

A conducting loop (in the shape of a rectangle) and with aresistance of 5 ohms moves along the surface of the paper as shownbelow. Within the region bounded by the dashed lines there isa magnetic field of 0.06 T going into the paper. a. When the loop is still entirely within the regionbounded by the dashed lines, what is the magnitude and direction ofthe current I that flows around the loop? b) When the loop is moving out of the field so that it ispartially removed from the field what is the magnitude anddirection of the current in the loop?

Explanation / Answer

   a.   When the loop isentirely inside the field, magnetic flux remains constant, hence nocurrent is induced in the loop.          I   =   0    b.   InducedEMF   =   - d/dt                                  =   -B * dA/dt    given   Magneticfield   B   =   0.06   T    rate of change ofarea   dA/dt   =   armlength normal to direction of velocity * velocity                                                    =   0.02* 60                                                    =   1.2   m2/s    Magnitude of inducedEMF   E   =   0.06 *1.2                                                       =   0.072   V    Magnitude of inducedcurrent   I   =   E /R                                                       =   0.072/ 5                                                       =   0.0144   A                                                       =   14.4   mA    Since loop is moving out, magnetic flux isdecreasing. According to Lenz's law, direction of induced currentmust be such that it opposes the decrease in magnetic field. To dothis, upper face of loop must behave as south pole, hence theinduced current will flow in clockwise direction.    Since loop is moving out, magnetic flux isdecreasing. According to Lenz's law, direction of induced currentmust be such that it opposes the decrease in magnetic field. To dothis, upper face of loop must behave as south pole, hence theinduced current will flow in clockwise direction.

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