A sliding conductor

Electricity and Magnetism Level 4

A horizontal conducting rod of mass \(m\) and length \(L\) is free to slide on two vertical conducting rails as shown, where there is a magnetised field of intensity \(B\) directed inside the screen and the resistance of the resistor is \(R\). Find the distance travelled by the rod after \(t\) seconds.

Inspiration.

\[d=\dfrac{mgR}{B^2L^2}\left(t-\dfrac{mR}{B^2L^2}\left(1+e^{-\frac{B^2L^2t}{mR}}\right)\right)\] \[d=\dfrac{mgR}{B^2L^2}\left(t-\dfrac{mR}{B^2L^2}\left(1-e^{-\frac{B^2L^2t}{mR}}\right)\right)\] \[d=\dfrac{mgR}{B^2L^2}\left(t+\dfrac{mR}{B^2L^2}e^{-\frac{B^2L^2t}{mR}}\right)\] \[d=\dfrac{mgR}{B^2L^2}\left(t+\dfrac{mR}{B^2L^2}\left(1+e^{-\frac{B^2L^2t}{mR}}\right)\right)\] \[d=\dfrac{mgR}{B^2L^2}\left(t+\dfrac{mR}{B^2L^2}\left(1-e^{-\frac{B^2L^2t}{mR}}\right)\right)\] \[d=\dfrac{mgR}{B^2L^2}\left(t-\dfrac{mR}{B^2L^2}e^{-\frac{B^2L^2t}{mR}}\right)\]

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A sliding conductor

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A sliding conductor

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations, examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.

Master advanced concepts through explanations,
examples, and problems from the community.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Master advanced concepts through explanations,
examples, and problems from the community.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.