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## Class 12 Physics (India)

### Unit 4: Lesson 12

Current loops as magnetic dipoles# Magnetic dipoles & dipole moment

A tiny current loop act's as a tiny magnet technically called a magnetic dipole. The strength of that tiny magnet, the magnetic dipole moment m, is given by m = NIA, giving the units - Ampere meter square. The magnetic dipole moment is a vector quantity and its direction is given by the right-hand thumb rule. Magnetic dipoles are different than electric dipoles in that, there are no magnetic monopoles, only dipoles. Created by Mahesh Shenoy.

## Want to join the conversation?

- what exactly does A mean here? in m = nIA ?(1 vote)
- What is the difference between M=NIA and M=n(2l)?Are they the same quantity?(1 vote)
- Technically, yes, they're the same thing. Here 'N' is the no. of loops, whereas 'n' is the loop per unit length (N/l). So multiplying it (n) with the total length 'l', we get 'N' again, i.e. the number of loops(1 vote)

## Video transcript

electric fields come from charges but where do magnetic fields come from what's inside a magnet that generates a magnetic field well let's find out let's start with something that we already know we know that a current carrying loop generates its own magnetic field and if you draw the field lines you will see that these field lines resemble that of a bar magnet in other words we can say a current loop behaves like a tiny magnet and it doesn't matter what that shape of the loop is it doesn't have to be circular as long as it's small enough or as long as you go far away from it that it loops that that current loop looks very small to you then the magnetic field lines will resemble that of a tiny magnet and so we can go ahead and now say that a current loop a current loop behaves like a tiny magnet tiny magnet but guess what tiny magnet is not a very technical term so you know how we say technically we say a current loop behaves like a magnetic dipole that's the technical term for it but it's the same thing okay it also feels good to say that go ahead say it current loop behaves like a magnetic dipole wow feels good right anyways this is great news because now if you want to use magnets in any experiment we don't need actual magnets we can get rid of them because we can use current loops and the advantage of a current loop is that you can control the strength of that tiny magnet for example if you increase the current and the advantage of this is that you can control the strength of the magnet if you make the current stronger you get a stronger magnetic dipole if you make the current weaker you get a weaker magnetic dipole so you can alter that strength and so that brings us to the next question what determines the strength of this tiny magnet or the magnetic dipole i mean current is definitely one of the things but what else determines the strength of this dipole and again there's a technical term for it so we're talking about strength strength of this magnet and the technical term for the strength is we call it moment so technically you would ask what determines the magnetic dipole moment okay and the symbol we use is m and clearly current is one of them so the magnetic moment is proportional to current but what else is it what else determines the magnetic moment well what about the number of loops that you use in your coil if you double the number of loops then you will have twice as much magnetic moment right it's as if you have twice if you as it's as if you have two loops and so it'll be double if you have n loops then it'll be n times more so the magnetic moment is also proportional to the number of turns that you have and it also turns out that the magnetic moment is proportional to the area of this loop it doesn't matter what shape it is it can be circular square rectangular but the area is what matters and so the area also determines the magnetic moment and if you're wondering how do we know that this is it like how do we know exactly this is the relationship we will derive this in a future video but as of now intuitively hopefully this makes sense and so that's how you calculate this is how we like to calculate the magnetic moment or the strength of this tiny magnet so the number of a number of loops multiplied by the current multiplied by the area so given this we can now look at the units of our magnetic moment can you quickly pause the video and write down the units of this go ahead give it a shot all right n has no units it's a number i is amperes and area is meter squared and so we represent the moment in ampere meter square so if somebody asks you how strong is your magnet this current loop how strong is it behaving like a magnet you say so many ampere meter squares that's how we represent the dipole moment okay here's a question for you do you think dipole moment should be a scalar quantity or a vector quantity what do you think well the magnetic fields certainly depend upon the orientation of a magnet and similarly it will depend upon the orientation and the direction of the current right so it makes sense to think of dipole moment as a vector quantity so now we need to ask ourselves how do we define the direction of the dipole moment well look over here over here the magnetic field is produced upwards at least on the axis you can sort of see the magnetic field is upwards so over here we could say that the direction of that dipole moment is upwards but how do you represent this in general how do we represent this in general well if you think in terms of a magnet if you imagine that this was a magnet then you could say that the magnetic type 4 moment is from south pole to north pole as you can see because the field lines inside the magnet run from south pole to north pole so that's one way in which we can represent that but let's forget about that hypothetical magnet if i were to just look at this loop and from there from there from you know define the direction of the moment how would i do that well this is where we can bring in our famous this is quite famous now right hand thumb rule you can see if you clasp your right hand in such a way that the four fingers represent the direction of the current then notice the thumb is showing the direction of the magnetic moment and so we can use our right hand thumb rule to tell you the direction of the magnetic moment so let me take another example let's see if you can use your right hand thumb rule to tell the direction let's say we had a current carrying loop this way so that the current is flowing in this direction can you pause the video and use your right hand and tell me what direction would be the magnetic moment in this case all right you would have to use your right hand clasp bit such that the four fingers run in this plane in this direction if i were to do that it would look somewhat like this notice the four fingers are going in the direction of the current and the thumb is pointing inwards so in this case we would say the magnetic moment is pointing into the screen so magnetic moment is a vector quantity all right the last question i have which could be probably the most important questions about dipoles is what's the difference between a magnetic dipole and an electric dipole remember electric dipoles electric dipoles were two charges one positive and one negative equal magnitude separated by some distance we call them the electric dipole and if you look at the field electric field produced by that notice it is so similar to our magnetic dipole field just to jog your memory for electric dipoles also we defined a moment the strength of that dipole we said that the electric dipole moment which was given by p symbol we used was p we said equals the charge the magnitude of the charge which is the same times the distance between these two charges this is how we defined our electric dipole moment and again the way we looked at the direction of the electric dipole moment over here we see again the dipole is sort of pointing upwards from negative to positive charge that's how we defined it over here okay now the big question that i want to ask you is what difference conceptually do you see between magnetic dipoles and electric dipoles what is the major difference that you might be seeing of course you might say formula is different units might be different but conceptually the major difference that i see it's important is when it comes to electric dipoles they are formed by putting one positive charge and one negative charge together we can call them monopoles because one one mono monopoles so two monopoles when you keep them together that's how we get electric dipoles but for magnetism notice we don't have monopoles magnet in magnetic fields we only have dipoles big difference and so it's for that reason you can see that electric fields start from one monopole and into the other monopole start from positive and end into negative always but for magnetism we don't have monopoles we only have dipoles and therefore you notice that they will always be you know they don't start from anywhere they won't end into anywhere they will always form closed loops in magnetism we only have dipoles no monopoles at this point you might say okay but what about inside a magnet magnets definitely have north and south so they do have monopoles right no even inside magnets the magnetic field is generated by current loops now you might say hey where are there current loops inside a magnet well remember everything has atoms and atoms are basically you can think of them as electrons zipping around positive charges now electron is a charged particle and as it moves we get a current and so the very fact that the electron is going around gives us a current loop which generates a magnetic dipole so notice even a single atom behaves like a magnetic dipole and it turns out that the electrons have a tendency to spin around its own axis now of course in reality the word spin at least for electrons means a very different thing but we don't have to worry too much about the details as of now we can just imagine the electrons are spinning around its own axis and when they do we again have a current loop because electron is a charge we can sort of have a current loop over there and that means a single electron itself behaves like a tiny magnetic dipole so notice that every single electron or you know atoms they all tend to behave like magnetic dipoles there are no monopoles anywhere and now if this is making you wonder somewhere in the back of your head but wait a second everything has atoms and electrons inside of it so shouldn't everything be magnets then you're on the right track the next step of course would be to dig into the atoms and think about what really happens at the atomic level and when the atoms come together to form objects but of course that's a story for another day but the point that i wanted to drive home over here is that everything when it comes to magnetic is dipoles we don't have magnetic monopoles so long story short current carrying loops behave like tiny magnets we call them dipoles and the strength of that tiny magnet which we call magnetic dipole strength is given by the product of the number of loops times the current times the area