Another Electromagnetic Induction Question

In summary, the conversation discusses a problem involving a metal bar on frictionless, inclined rails with a downward-directed magnetic field. The questions ask for the terminal speed of the bar, the induced current in the bar, the rate of electrical energy conversion to thermal energy in the bar, and the rate of work done on the bar by gravity. The individual attempted to use equations to solve the problem and made progress by considering a force diagram and equating the magnetic force to the x component of the force of gravity.
  • #1
Giuseppe
42
0
Again, this is a problem I got in my AP Physics Class can anyone help? I would really appreciate any help. My teacher didn't explain this concept too well.

A metal bar with length [tex] L[/tex], mass [tex]m[/tex], and resistance [tex]R[/tex] is placed on frictionless, metal rails that are inclined at an angle [tex] \theta[/tex] above the horizontal. The rails have negligible resistance. A uniform magnetic field of magnitude [tex]B[/tex] is directed downward. The bar is released from rest and slides down the rails.

a. What is the terminal speed of the bar?
b. What is the induced current in the bar when the terminal speed has been reached?
c. After the terminal speed of the bar has been reached, at what rate is electrical energy being converted to thermal energy in the resistance of the bar?
d. After the terminal speed has been reached, at what rate is work being done on the bar by gravity?


I attemped first to use the equations that
[tex]\varepsilon=BLv[/tex]
[tex] i=\frac{\varepsilon}{R}[/tex]
[tex]F_B=iLB.[/tex]

After some substitutions I find
[tex]F= \frac{B^2L^2v}{R}[/tex]
but what do I do next?
 
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  • #2
I think I made a little progress. After drawing a force diagram, I think I could say that the magnetic force = the x component of the force of gravity(i split gravity into components rather than anything else). so then i said that:

[tex]mg\sin{\theta}= \frac{B^2L^2v}{R}[/tex]

and then solved for [tex] v[/tex]. Would this be right for the terminal velocity?
 
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  • #3


To solve this problem, we can use the concept of electromagnetic induction. When a conductor moves through a magnetic field, an electric current is induced in the conductor. This current will experience a magnetic force, causing the bar to slow down until it reaches a terminal speed where the magnetic force is equal to the gravitational force.

a. To find the terminal speed, we can use the equation F_B = mg, where F_B is the magnetic force and mg is the gravitational force. We can rewrite this equation as B^2L^2v/R = mg, and solve for v to get the terminal speed v = mgR/B^2L^2.

b. To find the induced current, we can use the equation i = \varepsilon/R, where \varepsilon is the induced emf and R is the resistance of the bar. We can substitute in the value for \varepsilon from the first equation, \varepsilon = BLv, and solve for i to get i = BLv/R.

c. After the terminal speed has been reached, the bar is moving at a constant speed, so there is no change in kinetic energy. Therefore, all of the work done by the magnetic force is being converted into thermal energy in the resistance of the bar. The rate at which this energy is being converted can be calculated using the equation P = i^2R, where P is the power, i is the current, and R is the resistance. We can substitute in the values for i and R from part b to get P = (BLv/R)^2 * R = B^2L^2v^2/R.

d. After the terminal speed has been reached, the gravitational force is equal to the magnetic force, so the net work being done on the bar by gravity is zero. However, gravity is still doing work to maintain the bar's motion at a constant speed. The rate at which this work is being done can be calculated using the equation P = Fd/t, where F is the force, d is the distance, and t is the time. Since the bar is moving at a constant speed, we can use the equation d/t = v, and substitute in the value for F = mg to get P = mgv.

I hope this helps to clarify the concept of electromagnetic induction and how it applies to this problem. If you have any further questions, feel free to ask your teacher or consult additional resources for
 

Related to Another Electromagnetic Induction Question

1. What is electromagnetic induction?

Electromagnetic induction is the process of generating an electric current by moving a conductor through a magnetic field or by changing the magnetic field through a stationary conductor.

2. How does electromagnetic induction work?

Electromagnetic induction works by creating a changing magnetic field, which induces a current in a nearby conductor. This is due to the interaction between the magnetic field and the charged particles in the conductor.

3. What are some applications of electromagnetic induction?

Electromagnetic induction has many practical applications, including power generation in electric generators, wireless charging of devices, and induction cooktops.

4. What is Faraday's law of electromagnetic induction?

Faraday's law of electromagnetic induction states that the magnitude of the induced electromotive force (EMF) in a closed circuit is proportional to the rate of change of the magnetic flux through the circuit.

5. How is electromagnetic induction related to electromagnetic waves?

Electromagnetic induction is closely related to electromagnetic waves as they are both based on the interaction between electricity and magnetism. Electromagnetic waves are created by the acceleration of charged particles, which can also induce a current through electromagnetic induction.

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