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N. E. Fields. G. T. I. A. and. C. M. Forces. Magnetism: Overview. I Magnetic field exists; how does it affect matter ? II What is the origin of magnetic field ? III How are electric and magnetic fields related ?. Magnetic field lines. emerge from North poles
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N E Fields G T I A and C M Forces
Magnetism: Overview • I Magnetic field exists; how does it affect matter ? • II What is the origin of magnetic field ? • III How are electric and magnetic fields related ?
Magnetic field lines • emerge from North poles • enter at South poles • Magnetic field (B) is tangent to field lines • There is a corollary to electric field lines!
Lorentz Force Law Both the electric field and magnetic field can be defined from the Lorentz force law: The electric force is straightforward, being in the direction of the electric field if the charge q is positive, but the direction of the magnetic part of the force is given by the right hand rule.
It’s what came before QVC • So in very basic terms the force exerted on a particle is simply F= qvB Where F is the Force (newtons) q is the charge (in coulombs) v is the velocity and B is the strength of the magnetic field (in Teslas= 1 newton*second / coulomb * meter))
Right Hand Rule #1- in wire Current (I) through a wire produces a magnetic field (B) around the wire. The field is oriented according to the right hand grip rule.
Force on a moving charge • charge must be moving (no force if neutral) • charge must cut across field lines as it moves (no force if charge moves parallel to field) • for a given speed, greatest force occurs when v is perpendicular to B • for a given direction, greater speed means greater force Units of B are Tesla (T) Charge moving perpendicular to field lines
Magnetic Force • Force is perpendicular to velocity of particle • Force is perpendicular to field B • Since the force is acting at right angles to the motion, it does no work, so it cannot cause a particle to speed up or slow down.
Trajectories When moving in a uniform field, the path of a charge depends in a simple way on its direction with respect to the field. There are three cases: 1) Uniform motion (no acceleration) 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2) This leads to uniform circular motion
3) Both This leads to a superposition of cases 1 and 2. What do you get when you superpose circular motion perpendicular to the field with uniform motion along the field? Helix, with axis along field Even if the field is not uniform, charges will tend to circle around the local field lines as they drift along these same lines
Exercise: An electron is accelerated through a potential difference of 100 V and then enters a region of magnetic field .1 T, moving at right angles to the field. Find the radius of the circular orbit.
Force on current The moving charges within a wire are an easily accessible example of the magnetic force. Since we usually describe these charges in terms of their associated electric current, it makes sense to “rewrite” the magnetic force in terms of circuit parameters. X x x x x x x B v Assume there are N charges in L X x x x x x x L
Origin of magnetic field What can experience an electric field? charge What is the origin of the electric field? charges What can experience a magnetic field? Moving charge What is the origin of the magnetic field? Moving charges Electric currents are a readily available source of moving charges.
Field due to a long wire Direction determined by RHR #2: Thumb along current, then fingers curl along field lines OO Exercise: Find the magnetic field 10 cm from a wire carrying a current of 20 A.
Ferromagnetism • If moving charges are the source of magnetic fields, what are the moving charges in everyday iron magnets? • Orbital motion of electrons • While this motion does create magnetic fields, over a scale much larger than an individual atom, it will average out to zero since different atoms will have their electrons circulating in different directions. 2) Spin: electrons have an intrinsic spin; this motion will create magnetic fields also. Once again, over a large scale, these fields tend to cancel, except for certain materials. In some materials there is a residual interaction between the spinning electrons that tends to make them spin in same direction, and this causes the magnetic fields they create to add up, not cancel. These materials are said to be “ferromagnetic” and include iron, cobalt, nickel, and others. The interaction between spinning electrons has a finite range, and one finds that the tendency to line up is limited to a region large compared to atoms but still small compared to our everyday scale. These regions are called “domains”. To actually make a magnet, one has to align the domains, perhaps with a large external field.
A species of marine bacteria that live in the sediment at the bottom of the ocean actually contain roughly 5-20 magnetic particles aligned along the long axis of the organism. Should they be disturbed out of the sediment, their internal magnet aligns along the local earth field line and they swim back down to the sediment. In the northern hemisphere, the organism has a south pole at its anterior, while the opposite occurs in the southern hemisphere. A northern hemisphere organism brought to the southern hemisphere will swim to the surface!
