The Voyager I spacecraft moves through interstellar space...

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 $5.0-\mathrm{m}$-long antenna on the spacecraft is at right angles to the magnetic field, find the motional emf between its ends.

Key Concepts

Motional Electromotive Force (EMF)

Motional EMF refers to the potential difference generated when a conductor moves through a magnetic field. This happens because the moving charges within the conductor experience a force that separates positive and negative charges, creating an electric potential along the length of the conductor. The magnitude of this EMF is directly proportional to the speed of the conductor, the strength of the magnetic field, and the length of the conductor perpendicular to the field.

Magnetic Field

A magnetic field is a region in space where magnetic forces can be observed, typically described by a vector quantity that has both magnitude and direction. It exerts forces on moving charges and magnetic dipoles, which underpins many electromagnetic phenomena, including the production of motional EMF. The specific orientation and magnitude of the magnetic field relative to the motion of a conductor are key factors in determining the induced EMF.

Lorentz Force

The Lorentz force is the force exerted on charged particles when they move through electric and magnetic fields. In the context of motional EMF, the magnetic component of the Lorentz force acts on the moving charges within a conductor, causing them to accumulate at different ends of the conductor. This separation of charge leads to a measurable electromotive force, and its magnitude can be calculated using the cross product of the velocity of the conductor and the magnetic field.

Transcript

Please give Ace some feedback