A hammerhead shark (Figure P 21.55) has a 0.90-m-wide head....

A hammerhead shark (Figure $P 21.55)$ has a 0.90-m-wide head. The shark swims north at $1.8 \mathrm{m} / \mathrm{s} .$ Earth's $\vec{B}$ field at this location is $5.0 \times 10^{-5}$ T and points $30^{\circ}$ below the direction of the shark's travel. Determine the potential difference between the two sides of the shark's head.

Key Concepts

Earth’s Magnetic Field

Earth’s magnetic field provides a ubiquitous magnetic environment that affects moving conductors. Its strength, typically on the order of 10?? tesla, and its orientation relative to a conductor’s motion are important factors in determining the electromotive forces induced by movement through it. Understanding this natural field helps in analyzing phenomena in both practical and research-oriented contexts of magnetism and electromagnetism.

Vector Components in Electromagnetic Induction

When calculating the induced electromotive force, it is crucial to consider the vector nature of the velocity and magnetic field. Only the component of the velocity that is perpendicular to the magnetic field contributes to the induced voltage. This is typically expressed using the sine of the angle between the motion direction and the field, which shows how orientation affects the magnitude of the induced EMF.

Lorentz Force

The Lorentz force is the force on a charged particle moving in a magnetic field, described by the cross product of the particle’s velocity and the magnetic field vectors. It is responsible for the charge separation in a moving conductor which, in turn, generates an electromotive force. The force's magnitude depends on the charge, the speed of the particle, the magnetic field strength, and the sine of the angle between the velocity and the magnetic field.

Motional Electromotive Force (EMF)

Motional EMF refers to the voltage generated across a conductor as it moves through a magnetic field. This phenomenon arises from the separation of charge due to the Lorentz force acting on the free charges within the conductor, with the induced voltage being proportional to the magnetic field strength, the velocity of the conductor, and the effective length component that is perpendicular to the field.

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