Figure E27.42 The circuit shown in Fig. E27.42 is used to make a magnetic bal- b

Question

Figure E27.42 The circuit shown in Fig. E27.42 is used to make a magnetic bal- b 5.00n ance to weigh objects. The mass Battery WWW m to be measured is hung from the center of the bar that is in a uniform magnetic field of 1.50 T s X X X Bar X directed into the plane of the fig ure. The battery voltage can be adjusted to vary the current in the circuit. The horizontal bar is 60.0 cm long and is made of extremely light-weight material. It is connected to the battery by thin vertical wires that can support no appreciable tension; all the weight of the suspended mass m is sup- ported by the magnetic force on the bar. A resistor with R 5.00 n is in series with the bar; the resistance of the rest of the circuit is much less than this. (a) Which point, or b, should be the positive terminal of the battery? (b) If the maximum terminal voltage of the battery is 175 V, what is the greatest mass m that this instrument can measure?

Explanation / Answer

a) a should be the positive terminal.

then only current moves from left to right in the bar and magnetic force acts upward and balances the weight.

b) Current through bar, I = V/R

= 175/5

= 35 A

In the equilibrium

magnetic force on bar = weight of the hanging body

B*I*L*sin(90) = m*g

m = B*I*L/g

= 1.5*35*0.6/9.8

= 3.214 kg

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