# PHYS 2212 Module 9.2

## Lenz’s Law 9.2 Lenz’s Law

### Learning Objectives

By the end of this section, you will be able to:

• Use Lenz’s law to determine the direction of induced emf whenever a magnetic flux changes
• Use Faraday’s law with Lenz’s law to determine the induced emf in a coil and in a solenoid

### Lenz’s Law

The direction of the induced emf drives current around a wire loop to always oppose the change in magnetic flux that causes the emf.

Before we get into a discussion of Lenz’s law, take a few minutes to answer the following questions. Use what you know about energy conservation and what you have recently learned about Faraday’s law of induction to make your best guess as to the answers.

We’re going to perform a thought experiment in an effort to explain the minus sign in Faraday’s law: We will use what we know about magnetic fields produced by currents and what we now know about induced emf. Specifically:

1. A current produces a magnetic field and the direction of that B-field can be determined with the right hand rule (point your thumb in the direction of the current, wrap your fingers around the wire to show the direction of the circulating B-field)
2. A magnetic flux that changes in time will induce an emf that circulates around the area of the flux. If there is a conducting wire, the induced emf will drive a current in that wire.

So take this circular wire loop that is sitting in a uniform magnetic field that points into the page.

If the magnetic field is static, not changing, then there is no induced emf in the wire loop, so there is no induced current. But if that magnetic field changes, then there is a change in magnetic flux through the circular wire loop and there will be an induced emf which will drive a current. The question we want to answer is:

In which direction does the induced current flow? Clockwise or counterclockwise?

Here’s the thought experiment: Assume the magnetic field is increasing in strength. This means the magnetic flux is increasing so there will be an induced emf due to this change in flux. Let’s guess that the induced emf will be in a direction that will drive a current clockwise around the loop. You know that if there is a current in this wire loop, that current will produce a magnetic field at the center of the loop. This is a different magnetic field than the one in the picture, it’s coming from the induced current, so let’s call it the induced magnetic field. Using the right hand rule, what is the direction of this induced magnetic field if the induced current flows clockwise around the loop?

Go ahead and try to figure this out yourself.

From the right hand rule, you should have determined that the magnetic field coming from the induced clockwise current is into the page at the center of the loop. This induced magnetic field will add to the external magnetic field. So what will that do to the flux? The increasing magnetic field will increase the increasing flux even more. This greater increase in flux would induce a greater emf in the loop which would drive a stronger current, which would induce more magnetic field at the center of the loop, which would increase the change in flux, ….. I wrote that run-on sentence on purpose. Because this process would just happen indefinitely, where we would get more and more current induced in the loop. But this doesn’t happen in nature. It violates the law of conservation of energy. So the conclusion here is the induced emf must flow in a direction to oppose the change in flux. In this example, that would be counterclockwise. Let’s work through that to see why…

If the induced emf drives a counterclockwise current through the loop, that induced current will produce an induced magnetic field at the center of the loop that points out of the page. This would decrease the amount that the flux is changing. Remember that the flux is pointing into the page and increasing, so this induced current would take away from that increasing flux — which is what we mean by “opposing the change in flux”. If the flux is increasing, the opposite of that is decreasing. So we need the induced current to flow in a direction that will decrease the flux.

This is Lenz’s law — that the induced emf flows in a direction that will oppose the change in flux that produced it Practice!