# Terminal velocity

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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