A helicopter has blades with a length of 3.00 m extending...

A helicopter has blades with a length of $3.00 \mathrm{~m}$ extending outward from a central hub and rotating at $2.00 \mathrm{rev} / \mathrm{s}$. If the vertical component of the Earth's magnetic field is $50.0 \mu \mathrm{T}$, what is the emf induced between the blade tip and the center hub?

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Key Concepts

Electromagnetic Induction

Electromagnetic induction is the process by which a changing magnetic environment, whether due to a varying magnetic field or the motion of a conductor within a magnetic field, induces an electromotive force. This principle is central to the operation of many electrical devices, including generators and motors.

Rotational Kinematics

Rotational kinematics deals with the motion of objects rotating about an axis and establishes the relationship between angular velocity and linear velocity. The linear speed at any point on a rotating object is directly proportional to its distance from the axis of rotation, a key fact when determining the induced emf in rotating conductors.

Motional Electromotive Force (emf)

Motional emf is the voltage generated when a conductor moves through a magnetic field. This phenomenon occurs because the magnetic field exerts a Lorentz force on the free charges within the conductor, causing them to separate and create a potential difference across the conductor.

Lorentz Force

The Lorentz force is the force experienced by charged particles moving in a magnetic field, and is given by the cross product of the particle's velocity and the magnetic field. This force is fundamental in explaining how motion in a magnetic field can lead to the generation of an electromotive force.

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