In the circuit shown in the accompanying figure, the rod...

In the circuit shown in the accompanying figure, the rod slides along the conducting rails at a constant velocity $\overrightarrow{\mathbf{v}} .$ The velocity is in the same plane as the rails and directed at an angle $\theta$ to them. A uniform magnetic field $\overrightarrow{\mathbf{B}}$ is directed out of the page. What is the emf induced in the rod?

In the circuit shown in the accompanying figure, the rod slides along the conducting rails at a constant velocity
$\overrightarrow{\mathbf{v}} .$ The velocity is in the same plane as the rails and directed at an angle $\theta$ to them. A uniform magnetic field $\overrightarrow{\mathbf{B}}$ is directed out of the page. What is the emf induced in the rod?

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Key Concepts

Lorentz Force

The Lorentz force is the force exerted on a charged particle moving in a magnetic field. It is given by the cross product of the velocity vector and the magnetic field vector, and its direction is perpendicular to both. In conductors, this force separates positive and negative charges, leading to the development of an induced emf.

Vector Components and Projection

When evaluating induced emfs, especially in cases where conduction paths are not aligned with the velocity of motion, it is essential to consider the components of the velocity vector. Only the component of the velocity that is perpendicular to the conductor contributes to the magnetic force and the resulting induced emf.

Electromagnetic Induction

Electromagnetic induction is the phenomenon where a changing magnetic environment of a conductor induces an electromotive force (emf) in that conductor. This includes scenarios where the magnetic flux through a circuit changes due to motion through a magnetic field, leading to an induced voltage.

Motional EMF

Motional emf refers to the emf induced in a conductor as a result of its movement through a magnetic field. The induced voltage arises because free charges in the moving conductor experience a magnetic force, which drives them and creates a potential difference along the conductor.

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