welcome to I lecture online and today we're going to talk about magnetic fields and forces due to magnetic fields on moving charges and yes indeed when a charge exists in magnetic field and it's not moving there's no force on the charge and if a charge moves parallel to magnetic field the direction of magnetic field and also will be no force on the charge the only time that a charged a charged object or charge fields of force or experiences of force in a magnetic field is when the charge moves through the magnetic field perpendicular to the direction of magnetic field so I have a bunch of examples on the board here to try and figure out what the direction of the force will be on each of the charges as they're moving through the magnetic field remembering of course that the magnitude of the force can be found by taking the equation that the force on a moving charge is equal to the size of the charge Q times the cross product of the velocity of the charge times the magnitude of the magnetic field in the direction of magnetic field so force is Q V cross B and of course the when we want to find the magnitude of V cross B this can be written as the magnitude of the force is equal to Q times V times B times the sine of the angle between them now theta is the angle between the direction of the velocity of the charge in the direction of the B field and you can see then if the if the angle between them is 90 degrees which means if the direction of the velocity is perpendicular to the direction of magnetic field the sine of 90 degrees is 1 and then the magnitude is 4 simple will be QV B if the angle between them is not 90 degrees then of course the force will be less than Q V B by this factor and of course if the sine if the angle is zero degrees between the direction of the velocity and the direction of magnetic field then the sine of zero is zero and the magnitude of force will be zero accordingly all right so what we're going to do now is we're going to try and find the direction of the force on each of these charges you can see there's a charge here moving upwards charge here movement charger moving to the right also notice that some charges are positive some charges are negative and that does make a difference now the magnetic field is indicated by this B with an arrow on top of it so that's we sometimes call it the B field or a magnetic field and these arrows here are in the direction of the magnetic field here the fields to the right here it's up this means that the field is into the board it's like looking at the back of an arrow where you see the hairs in the back there so the B field is into the board here we're looking at the tip of the arrow so the B field is out of the board towards you here again the field is downward to feel this to the left here the field is out of the board and there to B field is into the board so based upon that what will be the direction of the forces of each of those eight charges in each of those eight different magnetic fields and I'll use a red pen to try and indicate it the way that's done is that if it's a positive charge use your right hand for the right hand rule if it's a negative charge you use your net in your left hand for for negative charges to find the direction of the of the force and so how do you do that well you take your hand and you point your fingers in the direction of the velocity of the charge and since it's a positive charge I'm using my right hand like so then you have to turn your hand whatever direction you need to so you can curl your fingers in the direction of the B field so I'm pointing upward and then I point this way to show the direction the B field so up for the velocity this way the B field and then my thumb points inward into the board so I can say then the force and I'll indicate that will across the force and will be into the board so velocity up be filled this way fours into the board looking at this example here of course I need to use my left hand because it's a negative charge I point my fingers in the direction of the velocity of the of the charge then I have to curl my fingers in direction to be feel of course I can't curl my fingers upwards have to turn my hand around I cannot curl my fingers upward and my thumb points into the board so here also the force on this charge will be into the board okay going to our next example here we have a B field that's into the board but oh I need to use my right hand because it's a positive chart take my right hand point my fingers in the direction of the velocity of the charge then I have to curl or turn my hand in such a way that I can curl my fingers towards the B field which is into the board and now my thumb points upward so I can see now that the force on this charge will be upward so go like this force is upward alright next example negative charge means I have to use my left hand I point my hand the direction of the velocity which is down now I have to turn my hand in such way that I can curl my fingers in direction of B field with some of the board so I'll turn my hand around this way poor my fingers outward and then my thumb points to the right which means that the force on that charge will be to the right alright next example here we have a positive charge so I use my right hand I point my fingers in direction of the velocity which is upward now I have to turn my fingers in the direction of B field which is downward ah but now we realize that the B field is down the velocity is up the angle between them is 180 degrees so we have an angle here that goes from there all the way to here which is theta equals 180 degrees and of course the sine of 180 degrees is zero and therefore there is no force so here we can say that force equal zero no force on that one alright next charge we have a negative charge so I use my left hand I point my fingers in the direction of the velocity which is done now with caramell fingers in the direction of the B field which is this way now even though it's not a 90 degree angle it's not a 180 degree angle so the sine of something between 90 and 180 is still a valid number somewhere between zero and one so we'll have some sort of force and my thumb is pointing outward so I can say that the force on this charge will be outward so force is out of the board I indicate that with a dot sometimes we indicate with that with a little circle around it like the tip of an arrow all right now next example positive charge I use my right hand I point my fingers in the direction of the velocity and then I have to turn my hand this way so I can turn my fingers in the direction of the B field which is out of the board and the force in that case will be up and finally last example here let move over this way we have a negative charge so we use left hand we point our fingers in the direction of the negative the velocity of negative charge now I have to turn my hand in such a way I guess I'll have to come this way sometimes Anna and atomically it's hard to do these things unless you stand correctly so fingers in the direction of the velocity then you point your fingers in direction of B fuel which is into the board and looks like my thumb is pointing this way so this charge will fill force in this direction there so hopefully they'll clears it up for you whenever you have a moving charge in a magnetic field the charge will feel a force as long as the the direction of the velocity is not parallel with the direction of magnetic field and to find the direction of the charge of the force on the charge you use your right hand or use your left hand right hand for positive charges left hand for negative charges point your fingers in direction of the velocity and curl your fingers in the direction of the B field your thumb will point in the direction of the force so that's called the left or right hand rule for finding the force on the charge or the direction of force on a moving charge in a magnetic field all right now we go on and actually start calculating some of the axial magnitudes of these forces and directional forces in some examples coming up in the next video