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Physics: High School18 chapters | 212 lessons

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Lesson Transcript

Instructor:
*David Wood*

David has taught Honors Physics, AP Physics, IB Physics and general science courses. He has a Masters in Education, and a Bachelors in Physics.

After watching this video, you will be able to explain what Ampere's Law is, and use Ampere's Law for a long, straight, current-carrying wire to solve problems. A short quiz will follow.

The full version of Ampere's Law is one of Maxwell's Equations that describe the electromagnetic force. **Ampere's Law** specifically says that the magnetic field created by an electric current is proportional to the size of that electric current with a constant of proportionality equal to the permeability of free space.

Stationary charges produce an electric field proportional to the magnitude of the charge. But moving charges produce magnetic fields proportional to the current (charge and movement).

The only problem with Ampere's Law is that it is a differential equation -- in other words, you need to do some calculus to use it. When you use Ampere's Law, you look at the particular situation you're in, plug in some values for that situation and complete the integral. This will get you an equation that fits the particular situation.

But instead of doing the messy calculus, we can look at the result of all that work. The situation we're going to look at in more detail is using Ampere's Law to find the magnetic field created by a long, straight, current-carrying wire.

The field created by a long, straight, current-carrying wire is in the form of concentric circles. And as you move further from the wire, those circles get further apart -- or in other words, the field gets weaker. We could create an equation for this by using Ampere's Law and doing some calculus. But we can actually derive this equation without any calculus at all.

Instead of an integral, we'll use a sum. The sum of all the magnetic field elements that make up the concentric circle: magnetic field *B* times the length of the element *delta-L* is equal to *mu-zero* (permeability of free space) times the current in the wire *I*. This is Ampere's Law.

Then realize that by summing all these elements up, your *delta-L* becomes the circumference of the concentric circle, 2pi*r*. Rearrange this to make the magnetic field the subject, and you get THIS final equation for the field created by a current carrying wire.

Here, *B* is the magnetic field at a particular point in space, measured in teslas. *Mu-zero* is the permeability of free space, which is a constant that's always equal to 1.257 x 10^-6. *I* is the current flowing through the wire, measured in amps. And *r* is the radial distance you are away from the wire, measured in meters. So you can use this equation to figure out the magnetic field strength at a distance *r* from a current-carrying wire.

Thanks to the equation, you can calculate the strength of the field. But what about the direction? For that, I need you to give me a thumbs up with your right hand. No, seriously, do it right now.

Using this diagram of a current-carrying wire, point your thumb in the direction the current is moving, in the direction of the arrow marked *I*. Now imagine curling your fingers around the wire, grabbing it. The direction your fingers point represents the direction the field lines point -- which way the arrows on the concentric circles go. This is called the right-hand rule, and it's vitally important you don't accidentally use your left hand, because you'll get exactly the wrong answer.

Okay, let's go through an example. Let's say you have a current-carrying wire pointing due-north. If the wire is carrying a current of 0.1 amps, what is the magnitude and direction of the magnetic field at a distance of 0.01 meters above the wire?

First of all, let's write down what we know. The current, *I*, is 0.1, the distance from the wire, *r*, is 0.01, and the permeability of free space is always 1.257 x 10^-6. Now all we have to do is plug these numbers into the equation and solve for *B*. Doing that gives us 2 x 10^-6 teslas. And that's our magnitude.

For the direction, you can draw the current on a piece of paper, pointing up towards the top of the page, which you can mark north. Now make a thumbs up with your right hand, point your thumb towards the top of the page too, and imagine curling your fingers around the wire. If you do it right, you'll see that your fingers would be pointing to your left underneath the wire, and to your right above the wire. If up the page is north, then to the right would be east.

So our final answer is 2 x 10^-6 teslas east.

The full version of Ampere's Law is one of Maxwell's Equations that describe the electromagnetic force. **Ampere's Law**, specifically, says that the magnetic field created by an electric current is proportional to the size of that electric current with a constant of proportionality equal to the permeability of free space. Stationary charges produce electric fields proportional to the magnitude of the charge. But moving charges produce magnetic fields, proportional to the current (charge and movement).

The only problem with Ampere's Law is that it is a differential equation -- in other words, you need to do some calculus to use it. But we can avoid this by looking at the result of all that calculus for a particular situation. If we study the magnetic field created by a long, straight current carrying wire, we get this final equation for the field created by a current carrying wire.

Here, *B* is the magnetic field at a particular point in space, measured in teslas. *Mu-zero* is the permeability of free space, which is a constant that's always equal to 1.257 x 10^-6. *I* is the current flowing through the wire, measured in amps. And *r* is the radial distance you are away from the wire, measured in meters. So you can use this equation to figure out the magnetic field strength at a distance *r* from a current-carrying wire. To get the direction of that field, we have to use the right-hand rule, and point our thumbs in the direction of the current.

After you have finished this lesson you should be able to:

- State Ampere's Law
- Calculate the magnetic field of a current carrying wire using Ampere's Law
- Recall the right-hand rule in calculating current direction

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Physics: High School18 chapters | 212 lessons

- Magnetic Force: Definition, Poles & Dipoles 6:09
- What is a Magnetic Field? 6:47
- How Magnetic Fields Are Created 6:19
- How Magnetic Forces Affect Moving Charges 6:13
- Electromagnetic Induction: Definition & Variables that Affect Induction 7:06
- Electromagnetic Induction: Conductor to Conductor & Transformers 7:43
- Electric Motors & Generators: Converting Between Electrical and Mechanical Energy 6:01
- Faraday's Law of Electromagnetic Induction: Equation and Application 8:12
- The Biot-Savart Law: Definition & Examples 6:19
- Ampere's Law: Definition & Examples 5:58
- Go to Magnetism in Physics

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