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A bar of mass m, length L, and resistance R slides without friction on parallel rails shown in the figure. A battery that maintains a constant emf ɛ is connected between the rails, and a constant magnetic field B is directed perpendicularly into the plane of the page. If the bar starts from rest at t = 0, (a) Find the current in the bar when it is moving at a speed v. (b) Write down the equation of motion of the bar (from F = ma), with v(t) of the bar as the unknown function of time. %3D (c) As t→ o, the speed v of the bar approaches a constant value vm. What is the value of vm?

A bar of mass m, length L, and resistance R slides without friction on parallel rails shown in the figure. A battery that maintains a constant emf ɛ is connected between the rails, and a constant magnetic field B is directed perpendicularly into the plane of the page. If the bar starts from rest at t = 0, (a) Find the current in the bar when it is moving at a speed v. (b) Write down the equation of motion of the bar (from F = ma), with v(t) of the bar as the unknown function of time. %3D (c) As t→ o, the speed v of the bar approaches a constant value vm. What is the value of vm?

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| A bar of mass m, length L, and resistance R slides without friction on parallel rails shown in the figure. A battery that maintains a constant emf ɛ is connected between the rails, and a constant magnetic field B is directed perpendicularly into the plane of the page. If the bar starts from rest at t = 0, (a) Find the current in the bar when it is moving at a speed v. (b) Write down the equation of motion of the bar (from F = ma), with v(t) of the bar as the unknown function of time. %3D (c) As t→ o, the speed v of the bar approaches a constant value vm. What is the value of vm? (d) Solve the equation in part (b) above, using a trial solution similar to that in an RC (or RL) circuit. Note that it has to be consistent with the result of part (c).
Transcribed Image Text:| A bar of mass m, length L, and resistance R slides without friction on parallel rails shown in the figure. A battery that maintains a constant emf ɛ is connected between the rails, and a constant magnetic field B is directed perpendicularly into the plane of the page. If the bar starts from rest at t = 0, (a) Find the current in the bar when it is moving at a speed v. (b) Write down the equation of motion of the bar (from F = ma), with v(t) of the bar as the unknown function of time. %3D (c) As t→ o, the speed v of the bar approaches a constant value vm. What is the value of vm? (d) Solve the equation in part (b) above, using a trial solution similar to that in an RC (or RL) circuit. Note that it has to be consistent with the result of part (c).
X X bar メ メ メ メ メ 入
Transcribed Image Text:X X bar メ メ メ メ メ 入
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