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UExcel Physics: Study Guide & Test Prep17 chapters | 188 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 lesson you will be able to explain what the Biot-Savart Law is, and use the simplified version to solve problems. A short quiz will follow.

Electric fields and magnetic fields might seem different, but they're actually part of one larger force called the electromagnetic force. Charges that aren't moving produce electric fields. But when those charges do move, they instead create magnetic fields. For example, a magnet is only a magnet because of moving charges inside it. And charges moving in an electric wire also produce magnetic fields. If you move a compass near to an electric wire, you'll find that the compass needle changes direction.

The **Biot-Savart Law** is an equation that describes the magnetic field created by a current-carrying wire, and allows you to calculate its strength at various points.

To derive this law, we first take this equation for electric field. This is the full version, where we use *muu-zero* over 4pi instead of the electrostatic constant *k*. Since we're looking at a wire, we replace the charge *q* with *I dl*, which is the current in the wire, multiplied by a length element in the wire. Basically it's treating this little chunk of the wire as our charge. And we also replace the electric field *E* with a magnetic field element *dB* because a moving charge produces a magnetic field, not an electric field.

Last of all, we have to realize that a current has a direction (unlike a charge). So we need to make sure the direction of the current affects our result. We do that by adding sine of the angle between the current and the radius. That way, if the wire is curvy, we'll take that into account. And that's it - that's the Biot-Savart law.

Using the Biot-Savart Law requires calculus. That's why there's a *dB* and *dl*. Those are infinitesimal magnetic field elements and wire elements. So we'd have to integrate with respect to those elements. But we can use a simpler version of the law for a perfectly straight wire.

If we straighten out the wire and do some calculus, the law comes out as *muu-zero I* divided by 2pi*r*. Or in other words, the magnetic field, *B*, measured in teslas is equal to the permeability of free space, *muu-zero*, which is always 1.26 x 10^-6, multiplied by the current going through the wire, *I*, measured in amps, divided by 2pi times the radius away from the wire, *r*, measured in meters. So this equation helps us figure out the magnetic field at a radius *r* from a straight wire carrying a current *I*.

The equation gives us the magnitude of the magnetic field, but magnetic field is a vector, so what about the direction? The magnetic field created by a current-carrying wire takes the form of concentric circles. But we have to be able to figure out if those circles point clockwise or counter-clockwise (say, from above). To do that we use a right-hand rule.

I want you to give the screen a thumbs up, right now. I'm serious - give the screen a thumbs up with your right hand. It has to be with your right hand. If you point your thumb in the direction of the current for this wire, your fingers will curl in the direction of the magnetic field. They'll follow the arrows of the concentric circles. And that's how you figure out the direction.

Okay, let's go through an example. Let's say you have a wire carrying a current of 0.1 amps, and you're asked to calculate the magnetic field at a distance of 0.5 meters from that wire. First of all, as usual, write down what we know. *I* is equal to 0.1 amps, and *r* is equal to 0.5 meters. We're asked to calculate the magnetic field, so *B* = ?. Everything else in the equation is a constant, so we can plug in the numbers and solve. The magnetic field *B* equals 1.26 x 10^-6 (that's *muu-zero*) multiplied by 0.1, divided by 2pi times 0.5 meters. Plug all that into a calculator and you get a magnetic field of 4*10^-8 teslas.

Finally, we need to find the direction. Based on this diagram showing the position we're interested in, what direction is this magnetic field pointing? Well, take your right hand, and form a thumbs up. Then point your thumb in the direction of the current - upwards towards the top of the screen. Now imagine curling your fingers around the wire... imagine physically grabbing the wire. Your fingers point in a counter-clockwise direction.

So at the point marked P on the image, the magnetic field is 4*10^-8 teslas and is pointed into the screen. (Or if this was a piece of paper, it would be into the page.)

And that's it -- we're done.

The **Biot-Savart Law** is an equation that describes the magnetic field created by a current-carrying wire, and allows you to calculate its strength at various points. It looks like this. Using the Biot-Savart Law requires calculus, but we can use a simpler version of the law for a perfectly straight wire.

The simpler version says that the magnetic field, *B*, measured in teslas, is equal to the permeability of free space, *muu-zero*, which is always 1.26 x 10^-6, multiplied by the current going through the wire, *I*, measured in amps, divided by 2pi times the radius away from the wire, *r*, measured in meters. So this equation helps us figure out the magnetic field at a radius *r* from a straight wire carrying a current *I*.

To figure out the direction of this magnetic field, we use a right-hand rule. If you point your thumb in the direction of the current in a wire, your fingers will curl around that wire in the direction of the magnetic field. This will show you which way the arrows go on the concentric circles.

So using the Biot-Savart Law and the right-hand rule, we can figure out all we need to know about the magnetic field created by a current-carrying wire.

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UExcel Physics: Study Guide & Test Prep17 chapters | 188 lessons

- Go to Vectors

- Go to Kinematics

- 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
- Faraday's Law of Electromagnetic Induction: Equation and Application 8:12
- Electromagnetic Induction: Definition & Variables that Affect Induction 7:06
- Electromagnetic Induction: Conductor to Conductor & Transformers 7:43
- The Biot-Savart Law: Definition & Examples 6:19
- Go to The Physics of Magnetism

- Go to Relativity

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