(a) What is the direction of the emf induced in the rod? (b) Find the magnitude of the emf induced in the rod. (c) Find the rate at which thermal energy is being generated in the rod.

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Problem 5
As shown below, a metal rod of length L = 10 cm is being pulled along horizontal, frictionless,
conducting rails at a constant velocity with v= 5.0 m/s.
B
The rails are connected at one end with a metal strip. A uniform magnetic field of magnitude
B = 1.2 T, directed out of the page, fills the region in which the rod moves. The resistance of the
rod is R = 0.402, and assume that the resistance of the rails and metal strip is negligibly small.
(a) What is the direction of the emf induced in the rod?
(b) Find the magnitude of the emf induced in the rod.
(c) Find the rate at which thermal energy is being generated in the rod.
(d) Find the magnitude of the external force on the rod that is needed to maintain the constant
velocity v.
(e) This set up is similar to the rail gun we looked at in a previous homework, but this time the
current is induced by the motion rather than provided by an external power source. When the
current in the rail gun is due to an external source and is constant, and we ignore the effects of
Faraday's law, we found that the rod has a constant acceleration. Describe the motion of the
rod if we now do include the effects of Faraday's (and Lenz's) law. Assume that the source of
the current is a battery or similar source that contributes to the total EMF.
The next two problems concern the induced magnetic field due to changing electric fields (Maxwell's
correction to Ampere's law)
Transcribed Image Text:Problem 5 As shown below, a metal rod of length L = 10 cm is being pulled along horizontal, frictionless, conducting rails at a constant velocity with v= 5.0 m/s. B The rails are connected at one end with a metal strip. A uniform magnetic field of magnitude B = 1.2 T, directed out of the page, fills the region in which the rod moves. The resistance of the rod is R = 0.402, and assume that the resistance of the rails and metal strip is negligibly small. (a) What is the direction of the emf induced in the rod? (b) Find the magnitude of the emf induced in the rod. (c) Find the rate at which thermal energy is being generated in the rod. (d) Find the magnitude of the external force on the rod that is needed to maintain the constant velocity v. (e) This set up is similar to the rail gun we looked at in a previous homework, but this time the current is induced by the motion rather than provided by an external power source. When the current in the rail gun is due to an external source and is constant, and we ignore the effects of Faraday's law, we found that the rod has a constant acceleration. Describe the motion of the rod if we now do include the effects of Faraday's (and Lenz's) law. Assume that the source of the current is a battery or similar source that contributes to the total EMF. The next two problems concern the induced magnetic field due to changing electric fields (Maxwell's correction to Ampere's law)
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