hello everybody my name is Iman welcome back to my YouTube channel today we're gonna go ahead and finish our electrostatics and magnetism chapter and we left off at the fifth objective our fifth objective is now going to involve special cases in electrostatics we're going to discuss equipotential lines and electric dipoles now first thing equal potential lines this is a line on which the potential at every point is the same so that is the potential difference between any two points on an equal potential line is going to be zero now drawn on paper equal potential lines may look like concentric circles surrounding a source a source charge in three-dimensional space these equal potential lines would actually be spheres surrounding the source charge now from the equation for electrical potential we can see that no work is done when moving a test charge from one point on an equal potential line to another Point okay work will be done in moving a test charge Q from one line to another but the work depends only on the potential difference of the two lines and not on the pathway taken between them now this is entirely analogous to the displacement of an object horizontally on a level surface because the object's height from the ground hasn't changed its gravitational potential energy is unchanged furthermore a change in the object's gravitational potential energy will not depend on the path taken from one height to another but only on the actual vertical displacement now with that we can also talk about electric dipoles much of the reactivity of organic compounds is based on separation of charge the electric dipole which results from two equal and opposite charges being separated as small distance from each other can be transient or permanent so the dipole that we see in this Vigor we have a charge that's plus q and minus Q they're separated by some distance D notice that plus q and minus Q our source charges and given the dipole we may want to calculate the electric potential at some point P near the dipole now the distance between the point in space and say positive Q is R all right and the distance between the point in space and minus Q is r with a little minus subscript this one has a little positive subscript all right and we we know that the collection the the that the um distance between the point in space and the midpoint of the dipole is R okay we know that for a collection of charges the electrical potential p is the scalar sum of the potentials due to each charge at that point in other words for points in space in space relatively distant from the dipole all right compared to D the product of R1 and R2 is approximately equal to the square of R and R1 minus R2 and that's going to be approximately equal to D cosine Theta Theta when when we plug these approximations all right we can get the following Expressions here all right so we have a couple of Expressions we can write all right here's the electrical potential energy equal to KQ difference in distances inverse distances okay we can also write this equation two right here KP okay Q well we could actually write it as k q R2 minus R1 over R1 R2 but then we can redefine it to have this P cosine Theta term all right um because we just said that it was equal to D cosine Theta all right it could be P or we can plug in what P equal actually is which is Q D here Q is going to be your charge D is the distance so this is the dipole moment all right this p is the dipole moment and it's equal to charge and distance so now we have these two equations and expressions that we can use um to help us tackle dipole related questions and this P equals QD the product of charge and separation distance is essentially what is defined as the dipole moment all right now let's do a practice problem very quickly this problem says the water molecule has a dipole moment of 1.85 Debbie calculate the electric potential due to water molecule at a point 89 nanometers away Along the axis of the dipole okay now because the question asks for the potential along the axis of the dipole along the axis all right Theta is going to be zero degrees all right and then we can take that we can substitute the values into the equation for the dipole potential V is equal to k q d over r squared cosine Theta all right or we can replace Q D and just write K dipole moment because we were given the dipole moment r squared cosine Theta all right now we can go ahead and plug in values into this problem all right um cosine of 0 degrees is just one so we're just doing V equals k p over r squared K is 8.99 times 10 to the nine newton times meter squared over coulomb squared we have P it's given to us 1.85 Debbie all right here we're going to introduce an important conversion that you should know how to go from Debbie to coulomb per meter so that the units cancel out properly one Debbie is 3.34 times 10 to the minus 30 coulombs per meter all right and that's all going to be divided by the distance 89 nanometers 89 times 10 to the minus 9 meters and that's going to be squared all right plug this into a calculator and what we get is 7.01 times 10 to the minus 6 volts all right now one very important equal potential line to be aware of is the plane that lies halfway between the positive and the and the negative charge this is going to be called the perpendicular bisector of the dipole now because the angle between this plane and the dipole axis is 90 degrees and cosine 90 degrees equals zero the electric uh the electrical potential at any point along this plane is going to be zero all right the magnitude of the electric field on the perpendicular bisector of the dipole can then be approximated all right I don't have this equation written but we're going to write it right here it can be approximated as e k times p over r k cubed all right so the electric field vectors at the point along the perpendicular bisector will point in the direction that's opposite to the dipole moment all right and this is defined directionally by physicists sometimes chemists have their own sort of Direction um frame of reference if you will now one more thing that we also want to talk about here is that the dipole is a classic example of a setup upon which torque can act so torque is a measure of the force that can cause an object to rotate around an Axis or pivot point in the context of our lesson so far torque is specifically going to be discussed here in relation to the dipole all right now in the absence of the electric field of an electric field the dipole axis can assume any random direct orientation however the electric dipole however when the electric dipole is then placed in a uniform external electric field each of the equal and opposite charges of the dipole they're going to experience a force and that force is exerted on it by that field now because the charges are equal and opposite the forces acting on the charges will also be equal in magnitude and opposite in direction and this is going to result in a situation of translational equilibrium there will be however a net torque about the center of the dipole axis and actually the net torque can be calculated from this equation right here torque equals dipole moment times electric field sine Theta e is the magnitude of the uniform external electric field Theta is the angle the dipole moment makes with the electric field all right sine Theta beautiful now with that that was objective five okay we're about to move into objective six which is all about magnetism but let's just provide a couple of quick points from what we've learned so far in regards to objective five we talked about equal potential lines they designate the set of points around a source charge or multiple Source charges that are going to have the same electrical potential they are always perpendicular to electric field lines and work will be done when a charged charge is moved from one equal potential line to another that work though is independent of the pathway taken Between the Lines no work however is done when a charge moves from a point on an equal potential line to another point on the same equal potential line all right then we also talked about dipoles two charges of opposite signs separated by a fixed distance D that generates an electric dipole in an external electric field an electric dipole is gonna experience and net torque until it is aligned with the electric field Vector all right an electric field will not induce any translational Motion in the dipole regardless of its orientation with respect to the electric field vector all right with that we can confidently move into objective six all right magnetism so any moving charge it's going to create a map magnetic fields may be set up by the movement of individual charges like an electron moving through space or by mass movement of charge in the form of a current through a conductive material like a copper wire or a permanent magnet the SI unit for magnetic field strength is Tesla T Tesla all right where one t is equal to one Newton Second mass per coulomb all right now the size of a Tesla unit is quite large so sometimes magnetic fields are sometimes measured in Gauss all right one Tesla is equal to 10 to the four Gauss so you can tell a much smaller unit for gas now all materials they can be classified as either diamagnetic paramagnetic or ferromagnetic diamagnetic materials are made of with no unpaired electrons and that have no net magnetic field all right these materials are slightly repelled by a magnet and so they can be called weekly anti-magnetic all right these are going to include things like wood plastic skin just to name a few things now the atoms of both paramagnetic and ferromagnetic materials um have unpaired electrons so these atoms do not have a net magnetic dipole moment but the atoms in these materials are usually randomly oriented so that the material itself creates no magnetic field paramagnetic materials will become weakly magnetized in the presence of an external magnetic field aligning the magnetic dipoles of the material with the external field but then upon removal of the external field the thermal energy of the individual atoms will cause the individual magnetic dipoles to just reorient randomly alright some paramagnetic materials include aluminum copper and gold now ferromagnetic material like paramagnetic materials have unpaired electrons but then they have permanent Atomic magnetic dipoles that are normally oriented randomly so that the material has no net magnetic dipole however unlike paramagnetic materials ferromagnetic materials will become strongly magnetized when they're exposed to a magnetic field or under certain temperatures these are going to include things like iron nickel and Cobalt all right so those are three important definitions that we need to know now in addition to that we also want to talk about magnetic fields because any moving charge creates a magnetic field we would certainly expect that a collection of moving charges in the form of a current through a wire would produce a magnetic field in its vicinity the configuration of the magnetic field lines surrounding a current carrying wire wire will depend on that shape of the wire okay so there's two special cases that you might encounter on the MCAT test long straight wire magnetic field problems or circular Loop wire magnetic field problems for an infinitely long and straight current carrying wire we can calculate the magnetic the magnitude of the magnetic field produced by the current eye in the wire at a perpendicular distance R from The Wire using this expression right here B is the magnetic field all right at a distance R from The Wire all right this mu is the permeability of free space it's equal to 4 pi times 10 to the minus 7 Tesla times meters over hey all I hear is the current okay this equation demonstrates an inverse relationship between the magnitude of the magnetic field and the distance from the current now straight wires will create a magnetic fields in the shape of concrete Rings or concentric Rings my apologies now to to then determine the direction of the field vectors you're going to have to use your right hand rule all right this is the right hand rule that relates to magnetism I have it right here okay you're going to point your thumb in the direction of the current you're going to wrap your fingers around the carrier the current carrying wire all right and then your fingers are going to mimic the circular field lines that are curling around the wire all right so this is one of them all right I don't think it's demonstrated properly here so thumb points in the direction of V current and then your fingers will wrap around your current carrying wire all right and that's going to point into and mimic the circular field lines that are curling around your wire all right now for the second case your circular Loop all right of current carrying wire of some radius R the magnitude of the magnetic field at the center of the circular Loop is given with this expression again B here is your magnetic field this is your permeability of free space again I is current and R is radius right your distance R from The Wire all right you're going to notice these two equations are really similar the obvious difference being that the equation for the magnetic field of the center of the circular Loop of the wire doesn't include this Pi factor in the denominator the less obvious difference is that the first expression gives the magnitude of the magnetic field at any perpendicular distance R from the current carrying wire while the second expression it gives the magnitude of the magnetic field only at the center of the circular Loop of current carrying wire with some radius r all right of course this will make a lot more sense when we do practice problems all right now something else that we want to talk about are obviously magnetic forces all right now that we've discussed magnetic fields and how they can be created let's examine the forces that are exerted by magnetic fields on moving charges so magnetic fields they exert Force only on other moving charges that is charges do not sense their own Fields they only sense the field established by some external charge or charges or collection of charges and so in our discussion of magnetic force on moving charges and on current current carrying wires we're going to assume the presence of a fixed and uniform external magnetic field all right and note that the charges they often have both electrostatic and magnetic forces acting on them at the same time the sum of these electrostatic and magnetic forces is known as the lorentz force now when a charge moves in a magnetic field a magnetic force may be exerted on it the magnitude of of that can be calculated using this expression right here all right Q is the charge V is the magnitude of the Velocity B is the magnitude of the magnetic field and Theta is the smallest angle between the velocity vector and the magnetic field Vector all right notice that the magnetic force is a function of the sine of the angle which means that the charge must have a perpendicular component of velocity in order to experience a magnetic force so if the charge is moving parallel or anti-parallel to the magnetic field it will not experience a magnetic force here we're going to introduce this other right hand rule this is the one that relates to Magnetic forces the one where you wrap your hand around around the direction of the thumb that you point in the current okay so the for magnetic fields you point your thumb all right in the direction of your current and then you wrap your hand around the current carrying wire all right so that's the right hand rule for determining um the magnetic field right the circular field lines that are curling around the wire all right four magnetic forces all right here you have this second right hand rule all right you're going to point your thumb in the direction of motion all right your finger here in the direction of the magnetic field and your other finger will be the current so if you have two of these all right you can determine the motion of the other one so thumb is velocity it indicates the direction of movement all right fingers are field lines all right fingers are parallel like the uniform magnetic field lines your palm should the Palm is the force on a positive charge all right and the back of the hand is the force on a negative charge so you can think of it like that so you can point your fingers in the appropriate Direction okay to deter so essentially to determine the direction of the magnetic force on a moving charge you're going to first position your right thumb in the direction of the Velocity then put your finger in the direction of the magnetic field line all right and then your palm will point in the direction of the force Vector for a positive charge whereas the back of your hand will point in the direction of the force Vector for a negative charge all right so force is moving forces on moving charges something else that we want to talk about is the force on a current carrying wire all right so it should come as no surprise that a current carrying wire that's placed in a magnetic field is also gonna experience a magnetic force so for a straight wire the magnitude of the force created by an external magnetic field can be calculated using this expression here I is the current L is the length of the wire B is the magnitude of the magnetic field and Theta here all right Theta is the angle between the length and the magnetic field all right here remember in the other one for force on moving charge Theta here is the angle between velocity and magnetic field alright so don't forget that don't confuse those two awesome the same right hand rule here can be used for a current carrying wire in a field as for a moving point charge okay just remember that current is considered the flow of positive charge okay so with that we have covered chapter 5 for MCAT physics let's summarize a couple of points here for magnetic fields and forces remember current carrying wires they create magnetic fields that are concentric circles surrounding the wire that's why we use this first version of the right hand rule all right external magnetic fields can exert forces on charges moving in any direction except parallel or anti-parallel to the field point charges May undergo uniform circular motion in a uniform magnetic field where the centripetal force is the magnetic force acting on the point charge and the direction of the magnetic force on a moving charge or carry current carry it current carrying wire is determined using the second hand rule that the second right hand rule that we've talked about and Remember the lorentz force is the sum of the electrostatic and magnetic forces acting on a body all right let me know if you have any questions comments concerns Down Below in the next video we'll tackle some practice problems other than that good luck happy studying and have a beautiful beautiful day future doctors