A rectangular loop of wire with dimensions 1.50 cm by 8.00...

A rectangular loop of wire with dimensions 1.50 cm by 8.00 cm and resistance $R$ = 0.600 $\Omega$ is being pulled to the right out of a region of uniform magnetic field. The magnetic field has magnitude $B =$ 2.40 T and is directed into the plane of $\textbf{Fig. E29.24}$. At the instant when the speed of the loop is 3.00 m/s and it is still partially in the field region, what force (magnitude and direction) does the magnetic field exert on the loop?

Key Concepts

Faraday's Law of Electromagnetic Induction

Faraday's law states that a changing magnetic flux through a loop induces an electromotive force (emf) in that loop. This principle is fundamental in understanding how motion relative to a magnetic field can generate an electrical potential difference across a conductor, which is the driving mechanism behind many electromechanical devices.

Lenz’s Law

Lenz’s law provides the direction of the induced current resulting from a change in magnetic flux. It states that the induced current will flow in such a way as to oppose the change that produced it. This principle is a consequence of the conservation of energy and is critical in determining the direction of the magnetic forces involved.

Motional EMF

Motional emf refers to the emf generated when a conductor moves through a magnetic field, which causes the magnetic flux through the conductor to change. This concept is key in understanding how mechanical motion can be converted into electrical energy and is quantitatively described by the product of the magnetic field strength, the speed of the movement, and the effective length of the conductor in the field.

Ohm’s Law and Induced Current

Ohm’s law relates the induced emf in the loop to the resulting current via the resistance of the circuit. When an emf is induced in a loop, the current is given by the emf divided by the resistance of the circuit. This relationship is essential for calculating the magnitude of the current that flows due to the induced emf.

Magnetic Force on a Current-Carrying Conductor

The magnetic force on a current-carrying conductor, described by the Lorentz force, is vital for understanding the net force acting on the loop. This force is computed as the product of the current, the magnetic field strength, and the length of the conductor segment in the magnetic field, and it acts perpendicular to both the direction of the current and the magnetic field. The direction of this force is determined by the right-hand rule.

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