How do I solve for the velocity of a metal rod in a magnetic field?

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SUMMARY

The discussion focuses on deriving the velocity of a metal rod sliding on frictionless rails within a magnetic field. The equation for velocity is established as v(t) = v0e^t/T, where T = mR/(Bl)², with variables defined as mass (m), length (l), initial speed (v0), magnetic field (B), and resistance (R). Participants emphasize the importance of understanding motional electromotive force (emf) to describe the rod's motion accurately. A resource link is provided for further clarification on the topic.

PREREQUISITES
  • Understanding of electromotive force (emf)
  • Familiarity with differential equations
  • Knowledge of magnetic fields and their effects on conductors
  • Basic principles of mechanics related to motion
NEXT STEPS
  • Study the concept of motional emf in detail
  • Learn how to derive differential equations for motion in magnetic fields
  • Explore the implications of resistance on the motion of conductive materials
  • Investigate the relationship between magnetic fields and induced currents
USEFUL FOR

Physics students, electrical engineers, and anyone interested in the dynamics of conductive materials in magnetic fields will benefit from this discussion.

delta_simon
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Homework Statement


mass=m
length=l
initialspeed=v0
magneticfield=B
Resistor=R

Homework Equations


A metal rod of mass m and length l slides on two parallell frictionless rails.
A uniform magnetic field is directed perpendicular to the plane of the rails.
There is no external agent applying a force to the rod.

Show that v(t) = v0e^t/T
where T = mR/(Bl)²

The Attempt at a Solution



I don't know where to start. Shall I construct a differentialequation including dt and dA? If not the solution I would be greatful for some hints.
 
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delta_simon said:
I don't know where to start. Shall I construct a differentialequation including dt and dA? If not the solution I would be greatful for some hints.

Do you realize that there will be a motional emf developed? If find that, you'll be able to describe the motion of the metal rod.

This link should help
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elevol.html#c3
 

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