Interstellar Magnetic Field The Voyager I spacecraft moves...

Interstellar Magnetic Field The Voyager I spacecraft moves through interstellar space with a speed of $8.0 \times 10^{3} \mathrm{m} / \mathrm{s} .$ The magnetic field in this region of space has a magnitude of $2.0 \times 10^{-10} \mathrm{T}$ . Assuming that the 5.0-long antenna on the spacecraft is at right angles to the magnetic field, find the induced emf between its ends.

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Key Concepts

Electromagnetic Induction

Electromagnetic induction is the process by which a changing magnetic environment generates an electromotive force or current in a conductor. It is a fundamental principle in electromagnetism and underlies the operation of generators, transformers, and many other electrical devices.

Motional Electromotive Force (EMF)

Motional EMF occurs when a conductor moves through a magnetic field, causing free charges within the conductor to experience a force. This force, due to the conductor’s velocity crossing the magnetic field, results in a voltage being induced across the ends of the conductor. The induced emf is proportional to the speed of the conductor, the strength of the magnetic field, and the effective length of the conductor within the field.

Lorentz Force

The Lorentz force is the force applied on a charged particle moving in a magnetic field, and it is given by the cross product of the particle's velocity and the magnetic field. In the context of motional EMF, the Lorentz force acts on the free charges in the moving conductor, separating them and thus creating an electric potential difference across the conductor.

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