Problem 5 An electric device is made of a closed conducting loop composed of fixed rails connected to a power supply, and a light rod of mass m placed perpendicular to the rails, as shown in Fig.4. The fixed rails have a much lower electrical resistance compared to that of the mobile rod, so you may assume that the loop has a constant resistance R at all times. The battery supplies a constant voltage Vo and the mobile rod, which can slide without friction on the fixed rails, is initially positioned very close to the battery, at L-0. A magnetic field B is applied perpendicular to the plane of the loop. Vo Figure 4 (a) Determine the direction of the applied magnetic field if the bar is to be pushed away from the battery. (b) Determine the absolute value and direction of the net current passing through the closed loop. You may answer in terms of given variables and the velocity v of the bar at any given time. (c) Establish and solve the differential equation satisfied by the velocity v of the rod. Hint: remember that Fnet = mā. (d) Determine the expression for the net current carried by the loop as a function of time and plot it. Explain the long-term behavior of the velocity of the rod, current in the loop and net force acting on the rod.
Problem 5 An electric device is made of a closed conducting loop composed of fixed rails connected to a power supply, and a light rod of mass m placed perpendicular to the rails, as shown in Fig.4. The fixed rails have a much lower electrical resistance compared to that of the mobile rod, so you may assume that the loop has a constant resistance R at all times. The battery supplies a constant voltage Vo and the mobile rod, which can slide without friction on the fixed rails, is initially positioned very close to the battery, at L-0. A magnetic field B is applied perpendicular to the plane of the loop. Vo Figure 4 (a) Determine the direction of the applied magnetic field if the bar is to be pushed away from the battery. (b) Determine the absolute value and direction of the net current passing through the closed loop. You may answer in terms of given variables and the velocity v of the bar at any given time. (c) Establish and solve the differential equation satisfied by the velocity v of the rod. Hint: remember that Fnet = mā. (d) Determine the expression for the net current carried by the loop as a function of time and plot it. Explain the long-term behavior of the velocity of the rod, current in the loop and net force acting on the rod.
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Transcribed Image Text:Problem 5
An electric device is made of a closed conducting loop composed of fixed rails
connected to a power supply, and a light rod of mass m placed perpendicular to the
rails, as shown in Fig.4. The fixed rails have a much lower electrical resistance
compared to that of the mobile rod, so you may assume that the loop has a constant
resistance R at all times. The battery supplies a constant voltage Vo and the mobile
rod, which can slide without friction on the fixed rails, is initially positioned very
close to the battery, at L-0. A magnetic field B is applied perpendicular to the plane
of the loop.
Vo
Figure 4
(a) Determine the direction of the applied magnetic field if the bar is to be pushed
away from the battery.
(b) Determine the absolute value and direction of the net current passing through
the closed loop. You may answer in terms of given variables and the velocity v of the
bar at any given time.
(c) Establish and solve the differential equation satisfied by the velocity v of the rod.
Hint: remember that Fnet = mā.
(d) Determine the expression for the net current carried by the loop as a function of
time and plot it.
Explain the long-term behavior of the velocity of the rod, current in the loop and
net force acting on the rod.
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