A copper bar of length h and electric resistance R slides withnegligible frictio

Question

A copper bar of length h and electric resistance R slides withnegligible friction on metal rails which have negligible electricresistance. The rails are connected on the right with a wire ofnegligible electric resistance, and a magnetic compass is placedunder this wire (the diagarm is a to view). The compass needledeflects to the right of north, as shown on the diagram. Throughout this region there is a uniform magnetic field Bpointing out of the page, produced by largecoils which are notshown. This magnetic field is increasing with time, and themagnitude is B= B0 + bt, where B0 and b areconstants, and at time t=0 you release the bar when it is adistance x from the right end of the apparatus. At that instant thebar is moving to the right with a speed v. (a) Calculate the magnitude of the initial current I in thiscircuit. (b) Calculate the magnitude of the net force on the bar justafter you release it. (c) Will the bar speed up, slow down, or slide at a constantspeed? Explain briefly.

Explanation / Answer

a.

dB/dt = B0

initial currrent i = induced emf /R = NAB0/R

b.force F = qv(B0+bt)

c. spped up

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