B field created by a long straight current carrying wire.

[hannaht]

Hi. I have a problem regarding a lab. experiment question.

Homework Statement

An alternating current is made to run through a long straight wire, thus creating a time varying B field in the region surrounding the wire. A small inductor coil is then placed near the wire. The voltage induced in the coil is measured as the distance of the coil from the wire is varied.
Then, the voltage induced in the coil is measured as the frequency of the alternating current through the long wire is varied.

Can someone help explain to me how the induced voltage in the inductor coil comes about. Also, how is the induced voltage (and thus B-field) dependent on the distance of the coil from the long wire, and on the frequency of the ac current flowing in the long wire?

(The full details of the experiment are in the attactment) Thanks.

Homework Equations

The Attempt at a Solution

 

[Valkarie]

The induced voltage in the inductor coil is due to Faraday's Law of Induction, which states that the voltage induced in a coil is equal to the rate of change of the magnetic flux through the coil. In this experiment, the changing B field created by the ac current running through the long wire will cause a changing magnetic flux through the inductor coil, resulting in an induced voltage. The induced voltage (and thus B-field) will be dependent on the distance of the coil from the long wire because the further away the coil is from the wire, the weaker the B-field will be. This will lead to a lower induced voltage in the coil. The induced voltage (and thus B-field) will also be dependent on the frequency of the ac current flowing in the long wire because the higher the frequency, the faster the changing B-field will be, resulting in a higher induced voltage.

 

[piercas]

Hello,

The induced voltage in the inductor coil is a result of Faraday's Law of Induction. This law states that a changing magnetic field will induce an electric current in a nearby conductor. In this case, the alternating current in the long straight wire creates a changing magnetic field around it, which in turn induces a voltage in the nearby inductor coil.

The induced voltage is dependent on the distance of the coil from the long wire because the closer the coil is to the wire, the stronger the magnetic field it will experience, resulting in a higher induced voltage. As the distance increases, the magnetic field weakens and so does the induced voltage.

The induced voltage is also dependent on the frequency of the alternating current because a higher frequency means a faster changing magnetic field, resulting in a higher induced voltage. Lower frequencies will have a slower changing magnetic field and therefore a lower induced voltage.

I hope this helps explain the concept behind the induced voltage in this experiment.