Relationship between magnetic field and current equation

Magnetic Field Formula

relationship between magnetic field and current equation

An electrical current is the transfer of electrical energy through a conductor, usually a metal wire. If that wire is in a magnetic field, a force is exerted on the wire. The law relating the magnetic field intensity H to its source, the current density J, is. boxed equation GIF # Note that by contrast with the integral statement of. The magnetic field due to a current carrying wire is given by: we will have to integrate the above equation and, thus adding the magnetic field.

relationship between magnetic field and current equation

They're coming out on this side of the wire. And they're going in, or at least my hand is going in, on that side. Hopefully that makes sense. Now, how can we quantify? Well, before we quantify, let's get a little bit more of the intuition of what's happening.

It turns out that the closer you get to the wire, the stronger the magnetic field, and the further you get out, the weaker the magnetic field.

Magnetic field created by a current carrying wire

And that kind of makes sense if you imagine the magnetic field spreading out. I don't want to go into too sophisticated analogies.

relationship between magnetic field and current equation

But if you imagine the magnetic field spreading out, and as it goes further and further out it kind of gets distributed over a wider and wider circumference. And actually the formula I'm going to give you kind of has a taste for that. So the formula for the magnetic field-- and it really is defined with a cross product and things like that, but for our purposes we won't worry about that.

You'll just have to know that this is the shape if the current is going in that direction. And, of course, if the current was going downwards then the magnetic field would just reverse directions. But it would still be in co-centric circles around the wire. But anyway, what is the magnitude of that field? The magnitude of that magnetic field is equal to mu-- which is a Greek letter, which I will explain in a second-- times the current divided by 2 pi r.

So this has a little bit of a feel for what I was saying before. That the further you go out-- where r is how far you are from the wire-- the further you go out, if r gets bigger, the magnitude of the magnetic field is going to get weaker.

And this 2 pi r, that looks a lot like the circumference of a circle. So that gives you a taste for it. I know I haven't proved anything rigorously.

relationship between magnetic field and current equation

But it at least gives you a sense of, look there's a little formula for circumference of a circle here. And that kind of makes sense, right? Because the magnetic field at that point is kind of a circle.

relationship between magnetic field and current equation

The magnitude is equal at an equal radius around that wire. Now what is this mu, this thing that looks like a u?

Physics equations/Magnetic field calculations - Wikiversity

Well, that's the permeability of the material that the wire's in. So the magnetic field is actually going to have a different strength depending on whether this wire is going through rubber, whether it's going through a vacuum, or air, or metal, or water. And for the purposes of your high school physics class, we assume that it's going through air normally. And the value for air is pretty close to the value for a vacuum.

And it's called the permeability of a vacuum. And I forget what that value is. I could look it up. But it actually turns out that your calculator has that value. So let's do a problem, just to put some numbers to the formula. So let's say I had this current and it is-- I don't know, the current is equal to-- I'm going to make up a number.

And let's say that I just pick a point right here that is-- let's say that that's 3 meters away from the wire in question. So my question to you is what is the magnitude in the direction of the magnetic field right there? Well, the magnitude is easy. We just substitute in this equation.

Therefore, the magnetic field lines point in the counter-clockwise direction, forming circles around the wire. If the magnetic field lines form clockwise circles in the plane of the page or screenwhat is the vector direction of the electric current? The magnitude of the electric current can be calculated by rearranging the magnetic field formula: The magnitude of the magnetic field is given in nano-Tesla.

The prefix "nano" meansand so. The magnitude of the magnetic field at the distance specified is thus: The magnitude of the electric current in the wire is 0. The direction of the electric current can be determined using the "right hand rule".

relationship between magnetic field and current equation

Axially symmetric current distribution and associated radial distribution of azimuthal magnetic field intensity. Contour C is used to determine azimuthal H, while C' is used to show that the z-directed field must be uniform. To see that there can be no r component of this field, observe that rotation of the source around the radial axis, as shown in Fig.

Magnetic field created by a current carrying wire (video) | Khan Academy

But an r component of the field does not reverse under such a rotation and hence must be zero. The H and Hz components are not ruled out by this argument. However, if they exist, they must not depend upon the and z coordinates, because rotation of the source around the z axis and translation of the source along the z axis does not change the source and hence does not change the field.

The current is independent of time and so we assume that the fields are as well. Hence, the last term in 1the displacement current, is zero.