To measure a magnetic field produced by an electromagnet,...

To measure a magnetic field produced by an electromagnet, you use a circular coil of radius $0.30 \mathrm{m}$ with 25 loops (resistance of $25 \Omega$ ) that rests between the poles of the magnet and is connected to an ammeter. While the current in the electromagnet is reduced to zero in $1.5 \mathrm{s}$, the ammeter in the coil shows a steady reading of 180 mA. Draw a picture of the experimental setup and determine everything you can about the electromagnet.

Key Concepts

Faraday's Law of Induction

This law states that a changing magnetic flux through a circuit induces an electromotive force (EMF) in the circuit. It is fundamental for understanding how a time-varying magnetic field in the electromagnet produces an electric response (current) in the coil through the relationship EMF = -N (d?/dt), where N is the number of turns in the coil.

Magnetic Flux

Magnetic flux is a measure of the amount of magnetic field passing through a given area. It is proportional to both the strength of the magnetic field and the area through which the field lines pass, considering the angle between the field and the normal to the surface. A changing flux is what induces the EMF in the coil according to Faraday’s Law.

Lenz’s Law

This 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 direction that its magnetic field opposes the change in the original magnetic flux, which is why a reduction or increase in the electromagnet’s current results in a current in the coil that resists the change.

Ohm’s Law in the Context of Induced Currents

Ohm’s Law relates the induced EMF, the current, and the resistance in the circuit through the equation EMF = I × R. In this experiment, knowing the resistance of the coil and the observed steady induced current allows for determining the magnitude of the EMF produced during the magnetic field’s decrease.

Coil Geometry and Area Calculation

The area of the coil, which is circular in shape, is a key factor in calculating the magnetic flux. The area is given by A = ?r², where r is the radius of the coil. This area, along with the magnetic field strength, determines the amount of flux and how significantly its change can influence the induced EMF.

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