What is the largest terminal voltage the battery can have without breaking the c

Question

What is the largest terminal voltage the battery can have without breaking the circuit at the supports?

Vmax= V

A thin 52.0 cm -long metal bar with mass 760 g rests on, but is not attached to, two metal supports in a uniform 0.460 T magnetic field, as shown in the figure . A battery and a 26.0 Omega resistor in series are connected to the supports. What is the largest terminal voltage the battery can have without breaking the circuit at the supports? Vmax= V

Explanation / Answer

the current which flows through the circuit feels force from the magnetic field (lifting) which should balance the gravitational force on the bar. F1=L*I*B F2=mg F1=F2 --> L*I*B=mg --> I=mg/(LB)=10*0.76/(0.52*0.46)=31.77 A Now we know that current of 31.77 A flows via the resistor R, then the voltage drop on R should be I*R=31.77*26=826 V This is the maximum voltage that can be applied, if it will be more, then the magnetic force will be bigger than gravitational one and the system will not be stable.

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