Lenz's law and direction of current

[whitewolfw2]

Homework Statement

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What is the direction of the magnetic field due to the induced current when the following changes are made to the initial field?
a. The field is switched off.
b. The field strength is doubled.
c. The direction of the field is reversed.

Homework Equations

Lenz's law?
"Any induced current in a loop will be in a direction such that the flux it creates will oppose the change in flux which produced it."

The Attempt at a Solution

I can find the direction that current flows in a coil when a magnet in inserted into, or removed from, a coil, using the right hand curl rule, but this question confuses me. Isn't it necessary to know the origin of the field so that you know where the lines of flux are expanding from or contracting towards? The field lines coming out of the page don't indicate the origin of field? Help understanding this concept much appreciated.

 

[CompuChip]

I don't think you need to know the exact source of the magnetic field.
For example in a) you turn off the magnetic field. In a sense, this is the same as adding a flux into the page. Therefore, by Lenz's law, the current in the loop will produce a current that causes a flux out of the page to cancel it. You can also look at it this way: there is currently a flux outward through the loop. When you suddenly take that away, a current will start flowing which tries to preserve that flux.

The direction of the current can now simply be found by - for example - the right hand rule (thumb along the field lines, fingers curl in the current direction).

 

[nlightner]

I would like to clarify that Lenz's law is a fundamental law of electromagnetism that states that the direction of an induced current in a closed loop will be such that it opposes the change in magnetic flux that produced it. In other words, the induced current will create a magnetic field that opposes the change in the original magnetic field.

To answer the question, we need to consider the direction of the induced current when the changes are made to the initial magnetic field. Let's assume that the initial magnetic field is coming out of the page, as shown in the diagram.

a. When the field is switched off, there will be no change in the magnetic flux, and therefore no induced current will be generated.

b. When the field strength is doubled, the magnetic flux will also double in strength. According to Lenz's law, the induced current will create a magnetic field in the opposite direction, which means that the current will flow in the opposite direction as well.

c. When the direction of the field is reversed, the magnetic flux will also be reversed. Again, according to Lenz's law, the induced current will create a magnetic field in the opposite direction, which means that the current will flow in the opposite direction as well.

In conclusion, the direction of the induced current will always oppose the change in the initial magnetic field, regardless of the origin of the field. I hope this clarifies the concept for you.