A Boeing 747 with a 65-m wingspan is cruising northward at 250 m / s toward Alaska. The B⃗ field

step 1 In the given problem, length of the wing span is given as 65 meter. The speed with which this ai

A Boeing 747 with a 65-m wingspan is cruising northward at...

A Boeing 747 with a $65-\mathrm{m}$ wingspan is cruising northward at $250 \mathrm{m} / \mathrm{s}$ toward Alaska. The $\vec{B}$ field at this location is $5.0 \times 10^{-5} \mathrm{T}$ and points $60^{\circ}$ below its direction of travel. Determine the potential difference between the tips of its wings.

Key Concepts

Motional Electromotive Force (EMF)

Motional EMF refers to the voltage generated across a conductor moving through a magnetic field. As the conductor cuts through magnetic field lines, free charges within it experience forces that cause charge separation. This separation creates a potential difference along the length of the conductor, depending on the magnetic field strength, the speed of the conductor, and the orientation of its motion relative to the field.

Lorentz Force

The Lorentz force is the force exerted on a charged particle moving in a magnetic field, and it is given by F = q(v × B). In the context of a moving conductor, this force acts on the free electrons (or charge carriers), pushing them to one end and creating a voltage difference. The direction and magnitude of this force depend on both the velocity of the conductor and the magnetic field, making it essential for understanding induced EMF.

Vector Decomposition of Magnetic Field Components

When analyzing the generation of motional EMF, it is important to consider the effective component of the magnetic field that is perpendicular to the direction of the conductor's motion. This involves decomposing the magnetic field vector into components relative to the direction of travel. Only the component perpendicular to the motion contributes to the induced EMF, hence proper vector decomposition is crucial for accurately determining the potential difference.

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