 write down dipole in a uniform magnetic field dipole in a uniform okay so what we have done till now is we have found out till now we have found out magnetic field due to a dipole moment but we haven't yet discussed but we haven't yet discussed what happens to a dipole inside a magnetic field okay so this is what we are going to study now we it's like this you finding electric field due to an electric dipole okay and then finding what will happen to the electric dipole in external electric field okay fine so similarly here we have found out the magnetic field due to a magnetic dipole moment and now we are finding what will happen to magnetic dipole moment in external magnetic field okay now you know just like electric dipole moment will experience a torque which is equal to p cross e this is torque on electric dipole moment similarly the magnetic field can create a torque on magnetic dipole moment which is equal to m cross b okay so torque magnetic torque will be 0 if angle between m and b is 0 or 180 degrees okay for example this is the magnetic dipole moment this is let us say m this could be due to solenoid due to bar magnet whatever it is it doesn't matter ultimately it is m only okay so suppose this is magnetic dipole moment m fine and you have a magnetic field also along the same direction so torque will be 0 okay now if magnetic dipole moment is like this and this is the magnetic field b again torque will be 0 okay then what is the difference between these two scenarios how they are different now let us see if this is the magnetic dipole sorry let us say this is the magnetic field b okay and what you're doing is you're taking a dipole moment and you're rotating it a little bit suppose you rotate it in such a way that this angle is theta okay now tell me which direction the magnetic moment will experience the torque will it increase the theta or it will it decrease the theta the torque which this magnetic dipole moment will feel just message it increase or decrease Koshal is saying that it will increase the angle like if if I just keep it at angle theta with the magnetic field the angle will increase as in automatically okay Rithvik is also saying same thing automatically it will start rotating that direction all of you anybody says that it will decrease okay Vaishnavi is having an opposing point it will decrease anyways the answer is that it will decrease you can see that there are two vectors right this is one vector m and this is another vector b so if you consider the cross product which is m cross b which direction that direction of this cross product will be it will be clockwise isn't it it will be clockwise so magnetic dipole moment m will feel a clockwise torque m cross b and that is the reason why theta will decrease Rithvik and Koshal are you clear now right so that is why it will decrease okay so it will try to regain theta equal to 0 degrees okay so it tries to go back to its original position okay now let us see this if if let us say this is the magnetic field okay if this is the magnetic field and this was the original position of the magnetic dipole moment m fine right now the angle between magnetic dipole moment and magnetic field is 180 degree so torque is zero but then if you rotate it slightly like this okay now if this is angle theta now what will happen it will try to increase or decrease the angle theta the torque on m will it increase the angle theta or decrease the angle theta theta is the angle which is shown now Koshal and Rithvik will not answer first they will see don't become conscious just keep interacting you can message anything okay just reply whatever comes in your mind theta will increase or decrease yes now it will increase so the torque felt by the dipole again will be in clockwise direction look at it m cross b okay so because of that theta will increase so what will happen this will just completely rotate and align itself like this it will try to try to go to theta equal to zero okay so it flips okay so this is unstable equilibrium this is unstable and this is stable although both of them they are equilibrium both of them torque is zero they both are in equilibrium but one is stable equilibrium which again go back to its original position and the other one is unstable equilibrium you know we just slightly nudge it and it will completely flip over fine so that is a difference between you know theta equal to zero and theta equal to 180 degree okay now one thing you need to be clear here is that you know I I'm telling you something different here if this is magnetic dipole moment m okay now here are two locations one and two first tell me which direction the magnetic field will be at point number one this this this or that a b c or d all of you please type at this point which direction the magnetic field will be because of this exactly it will be a only now tell me at point number two a b c t which direction at point two this point what is the correct direction of magnetic field correct so two is a point which is on equatorial plane two is a point which is on equatorial plane so magnetic field if you recall the formula it was equal to mu naught by 4 pi minus m by r cube along the equatorial line so there is a minus sign fine so that is why on this point point two sees the correct direction magnetic field there is a minus sign negative direction of m m is along a direction minus m is along c direction getting it so remember these things okay now tell me this point that's one quickly a b c d you know which directions a b c d r it will be along a okay this point it will be along c fine so I hope this is very clear now okay good let us now take up a numerical long time we have done a question now first I will draw a diagram all of you draw with me draw a circle which is as nice looking as this you can't draw a better circle this is P first let us draw everything then I'll tell you what is the question fine so this is the figure I hope all of you have drawn it should I read out the question okay the question goes like this the figure shows a small magnetized needle P plays at a point oh so there is a dipole moment P which is fixed at the center this is a dipole moment that is fixed this is P direction is clearly shown this is fixed at the center okay now what you're doing is you are taking Q Q is another dipole moment okay Q is another dipole moment that you're taking and you are placing it at six different locations as shown fine so you can place it at Q 1 then you can place it at Q 2 Q 3 Q 4 Q 5 and Q 6 so six different places you can place the capital Q dipole moment okay you need to find out the first question is which configuration is not in equilibrium so we have learned about the equilibrium already we have learned about two types of equilibrium unstable and stable both are equilibrium only but different kinds of equilibrium so right now I am not differentiating between the kind of equilibrium okay I am just asking you which configuration are not in equilibrium you can say P and Q 3 P on and Q 6 like this okay so just think over it and message once you get quickly vegetables saying P and Q 1 not in equilibrium let's see what is a magnetic field direction due to P at Q 1 at Q 1 at this location the direction of magnetic field due to P will be downwards it is equatorial plane okay so magnetic field is downward so angle between this magnetic field and this Q 1 dipole moment is 90 degree so m cross B is not zero so it will experience a torque so P and Q 1 and P and Q 2 both here also the angle is 90 degree between magnetic field and dipole moment okay so both P Q 1 and P Q 2 they have they are not in equilibrium because angle is 90 degree P Q 1 and P Q 2 this is the answer fine now can you find out which of the configuration so Q 1 and Q 2 they are not in equilibrium so there are four configuration that are in equilibrium Q 3 Q 4 Q 5 and Q 6 you need to find which one are stable configuration and which one are unstable configurations first message the stable configuration the other one will automatically be unstable okay so if I take P Q 5 if I take P and Q 5 what is the direction of magnetic field due to P at location Q 5 it is this way fine and Q 5 is in which direction that is in this way so angle is 180 degrees this is not stable this is unstable okay so unstable is P Q 5 because angle between magnetic field due to P and the dipole moment which is Q 5 is 180 degrees the P Q 5 is unstable what about P Q 3 Simon deleted the message okay tell me P Q 3 P Q 3 is it stable or unstable quickly the magnetic field due to P at Q 3 will be in which direction downside isn't it so angle between this and that is 0 degree so P Q 3 is stable okay now let us take P and Q 6 this is along the axis so along the axis magnetic field due to a dipole is along the direction of dipole so P Q 6 will be stable because magnetic field at a location of Q 6 will be along the direction of Q 6 the P Q 3 and P Q 6 they are stable and you can see that P Q 4 will be unstable because magnetic field due to P will be in upward direction and Q 4 is downward direction so angle is 180 degrees so this is unstable P Q 4 getting it so like this you can analyze this particular scenario okay right so let us move forward