A thin, 54.0 cm long metal bar with mass 770 g rests on, but is not attached to,

Question

A thin, 54.0 cm long metal bar with mass 770 g rests on, but is not attached to, two metallic supports in a uniform magnetic field with a magnitude of 0.440 T, as shown in the figure (Figure 1). A battery and a resistor of resistance 21.0 Ohm are connected in series to the supports. What is the largest voltage the battery can have without breaking the circuit at the supports? V = _____ V The battery voltage has the maximum value calculated in part (a). If the resistor suddenly gets partially short-circuited, decreasing its resistance to 2.00 Ohm, find the initial acceleration of the bar. a = _____ m/s^2

Explanation / Answer

(a) If the cicuit do not break then the force on the bar must be balanced.
the force on the bar are gravity force which would act downward and the magnetic force which will act upward.
the magnetic force will be given by (Fm) = ILB
That must be equal to the gravity force = mg = 0.77*9.81
ILB = 0.77*9.81
I*0.54*0.44 = 0.77*9.81
I =31.792 A
this will be the maximum current that would pass from the circuit without breaking it.
Hence the voltage will be = IR = 31.792*21 = 667.625 V
This will be the maximum voltage that can be applied.
(b) If resistance would decrease to the 2 ohm then the current in the circuit will be
i = V/R = 667.625 / 2 = 333.8125 A
Now the magnetic force will be = iLB = 333.8125*0.54*0.44 = 79.314 N
Gravity force = 0.77*9.81 = 7.554 N
Net force ma = Magnetic force - gravity force
ma = 79.314 - 7.554 = 71.76
a = 71.76/0.77 = 93.195 m/s2

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