A strong electromagnet produces a uniform field of 1.60 T...

A strong electromagnet produces a uniform field of $1.60 \mathrm{~T}$ over a cross-sectional area of $0.200 \mathrm{~m}^{2}$. A coil having 200 turns and a total resistance of $20.0 \Omega$ is placed around the electromagnet. The current in the electromagnet is then smoothly decreased until it reaches zero in $20.0 \mathrm{~ms}$. What is the current induced in the coil?

Key Concepts

Lenz's Law

This principle 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 direction that its own magnetic field opposes the change in the magnetic flux that produced it, ensuring the conservation of energy within the system.

Faraday's Law of Electromagnetic Induction

This law states that a change in the magnetic flux through a closed circuit induces an electromotive force (EMF) in that circuit. It is a cornerstone of electromagnetic theory that relates the rate of change of the magnetic environment of a circuit to the voltage produced across it.

Magnetic Flux

Magnetic flux quantifies the total magnetic field passing perpendicularly through a given area. It is calculated by multiplying the magnetic field strength by the area it penetrates and the cosine of the angle between the field direction and the area's normal. Understanding magnetic flux is critical to determining how changes in the magnetic field impact the induced EMF.

Ohm's Law

Ohm's Law relates the voltage in a circuit to the current flowing through it and the resistance of the circuit. In the context of electromagnetic induction, once the EMF is determined from the change in magnetic flux, Ohm's Law is used to compute the magnitude of the induced current by dividing the induced voltage by the resistance of the circuit.

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