2.015 What If? Suppose the magnetic field has an initial value of 3.10 T at time t = 0 and increases at a constant rate of 0.500 T/s. The bar starts at an initial position x = 0.100 m to the right of the resistor at t = 0, and agaid moves at a constant speed of 1.55 m/s. Derive time-varying expressions for the following quantities. (e) the current through the 8.000 resistor R (Use the following as necessary: t. Assume I(t) is in A and t is in s. Do not include units in your answer.) I(t)= 0.50709 +1.55t x The magnetic field is increasing linearly with time. Can you find an expression for the magnetic field at any time? Similarly, can you find an expression for the x-position of the bar at any time, knowing it moves at constant speed? Using these, how does the flux through the loop depend on time? From your expression for flux, can you find the emf, and then the current, at any time? A (f) the magnitude of the applied force Fapp required to keep the bar moving at a constant speed (Use the following as necessary: t. Assume Fapp (t) is in N and t is in s. Do not include units in your answer.) Fapp(t) = N
2.015 What If? Suppose the magnetic field has an initial value of 3.10 T at time t = 0 and increases at a constant rate of 0.500 T/s. The bar starts at an initial position x = 0.100 m to the right of the resistor at t = 0, and agaid moves at a constant speed of 1.55 m/s. Derive time-varying expressions for the following quantities. (e) the current through the 8.000 resistor R (Use the following as necessary: t. Assume I(t) is in A and t is in s. Do not include units in your answer.) I(t)= 0.50709 +1.55t x The magnetic field is increasing linearly with time. Can you find an expression for the magnetic field at any time? Similarly, can you find an expression for the x-position of the bar at any time, knowing it moves at constant speed? Using these, how does the flux through the loop depend on time? From your expression for flux, can you find the emf, and then the current, at any time? A (f) the magnitude of the applied force Fapp required to keep the bar moving at a constant speed (Use the following as necessary: t. Assume Fapp (t) is in N and t is in s. Do not include units in your answer.) Fapp(t) = N
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Part E and F only
Transcribed Image Text:In the figure below, a steel bar sitting on two parallel metal rails, connected to each other by a resistor, is pulled to the right with a constant force of magnitude Fapp = 1.30 N. The friction between the
bar and rails is negligible. The resistance R = 8.000, the bar is moving at a constant speed of 1.55 m/s, the distance between the rails is l, and a uniform magnetic field B is directed into the page.
Fapp
(a) What is the current through the resistor (in A)?
0.502
✓ A
(b) If the magnitude of the magnetic field is 3.10 T, what is the length { (in m)?
0.8356
m
(c) What is the rate at which energy is delivered to the resistor (in W)?
2.015
✓ W
(d) What is the mechanical power delivered by the applied constant force (in W)?
2.015
✓ W
What If? Suppose the magnetic field has an initial value of 3.10 T at time t = 0 and increases at a constant rate of 0.500 T/s. The bar starts at an initial position xo = 0.100 m to the right of the
resistor at t= 0, and agaid moves at a constant speed of 1.55 m/s. Derive time-varying expressions for the following quantities.
(e) the current through the 8.000 resistor R (Use the following as necessary: t. Assume I(t) is in A and t is in s. Do not include units in your answer.)
I(t)= 0.50709 + 1.55t
x
The magnetic field is increasing linearly with time. Can you find an expression for the magnetic field at any time? Similarly, can you find an expression for the x-position of the bar at any time,
knowing it moves at constant speed? Using these, how does the flux through the loop depend on time? From your expression for flux, can you find the emf, and then the current, at any time? A
(f) the magnitude of the applied force Fapp required to keep the bar moving at a constant speed (Use the following as necessary: t. Assume Fapp(t) is in N and t is in s. Do not include units in your
answer.)
N
Fapp(t) =
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