Conducting rod moving on an inclined rail and electromagnetic induction

Problem Statement

Two smooth, parallel conductive rails are fixed at a distance L, inclined at an angle $\theta$θ with respect to the horizontal plane. A resistor with resistance $R$R is connected to the highest point of each rail. A uniform magnetic field (magnetic flux density $B$B) is applied to the entire inclined plane formed by the rails, perpendicular to the incline and directed upward.

A conducting rod of mass $m$m is placed on these rails perpendicular to the rails and released gently. The conducting rod slides down the incline along the rails. Assume that the resistance of the conducting rod and rails, the self-inductance of the circuit, and air resistance are all negligible, and the magnitude of the acceleration due to gravity is $g$g.

After a sufficient amount of time has elapsed since the release of the conducting rod, it begins to move in a straight line at a constant velocity $v$v. Find the algebraic expression for the magnitude of this velocity $v$v.

Constraints

• $m = 0.200 \text{ kg}$m=0.200 kg
• $g = 9.80 \text{ m/s}^2$g=9.80 m/s2
• $\theta = 30.0^\circ$θ=30.0∘
• $R = 4.00 \text{ }\Omega$R=4.00 Ω
• $B = 0.700 \text{ T}$B=0.700 T
• $L = 1.00 \text{ m}$L=1.00 m

Input Format

Calculate the magnitude of the velocity of the conducting rod $v \text{ [m/s]}$v [m/s] after a sufficient amount of time has elapsed, and input a natural number representing that value.