Terminal velocity

Electricity and Magnetism Level 3

A system of long, parallel conducting rails is set up in the vertical plane and joined at both the ends by resistors as shown in the figure. A uniform magnetic field exists perpendicular to the plane of the rails denoted by \( \vec{B} \). A rod whose length is equal to the separation between the rails is allowed to fall freely and attain a terminal velocity. If the powers dissipated by the resistors \(R_1\) and \(R_2\) at steady state are \(0.76 \text{ W}\) and \(1.2\text{ W}, \) respectively, then what is the terminal velocity of the rod?

Details and Assumptions

  • The length and mass of the rod are 1 m and 0.2 kg.
  • The acceleration due to gravity is \(9.8\text{ m/s}^2\).
  • The magnitude of the magnetic field is 0.6 T.
  • The rails are long enough so that the steady state conditions can be easily analysed.

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