F = q v B. F = q E + q v B. = q v B F B. F = q vbsinφ. Lorentz. Bar Magnets. Right Hand Rule. The Magnetic Force. v +q. x x x x x x x x x x x x B

Transcription

1 ar Magnets ar magnet... two poles: and Like poles repel; Unlike poles attract. Magnetic ield lines: (defined in same way as electric field lines, direction and density) Attraction The unit for magnetic field is Tesla (T): 1 T = 1 = 1 = 1 C m / s C / s m A m A common unit gauss (G): 1 G = 1-4 T 2/2/12 1 ~Earth s surface field! Repulsion Lorentz = q E + q = q = q sinφ 2/2/12 2 Right Hand Rule Direction of is perpendicular to plane containing &. f q is positie, has the same sign as x. f q is negatie, has the opposite sign of x. The Magnetic orce = q The direction of the force is: is neer parallel to. can only change the direction of the particle not the speed. 2/2/12 3 q 2/2/12 4 1

2 Magnetic orce on a Current-Carrying Wire Top iew of Current-Carrying ar liding on two current carrying frictionless rails in a magnetic field. V + 2/2/12 5 TH A ORM O ELECTRC MOTOR, TURG ELECTRCAL TO MECHACAL EERGY motion by reersing Direction of, by reersing V ote that this example assumes that the magnetic field caused by the currents in the rails is negligible compared to the external magnetic field shown. The length L is the distance between the rails, where is and where the current flows in the green bar. DEMO 2/2/12 6 Motion of a Point Charge in a Magnetic ield cannot change of a charged particle. cannot change the kinetic energy of a charged particle. can only change the direction of a particle. Trajectory in Constant Magnetic ield uppose charge q enters field with elocity as shown below. What will be the path q follows? q R glow of ionized gas 2/2/12 7 2/2/12 8 2

3 Motion of a Point Charge in a Magnetic ield Period of Circular Motion The period of the motion is or, the angular frequency 2/2/12 9 2/2/12 1 Mass pectrometer ons of different masses can hae the same charge q and the same elocity. f we shoot them to a uniform magnetic field perpendicularly, question: The circular trajectories followed by the ions once they enter the field would show: Mass pectrometer (ons with same KE) The purpose of a mass spectrometer is to separate ions by mass and measure the mass of each type of ion. f positie ions start from rest and moe through a potential difference, V, the ions kinetic energy when they enter the magnetic field equals their loss in potential energy: What kind of charge do the ions in the picture hae? 2/2/ /2/

4 Mass pectrometer (ons with same KE) Working with both equations : irst sole for the elocity on the first one, Then substitute it on the kinetic energy equation A mass spectrometer can be improed if instead of haing ions with the same kinetic energy entering the field we hae ions with the same elocity. 2/2/12 13 Combine an Electric ield and a Magnetic ield f we shoot charged particles into a region of space that has both an electric and a magnetic field, we would end up with a net electro-magnetic force that is equal to the ector sum of the electric and magnetic forces acting on the charge: = E + = qe + q A ery interesting effect can be achieed when we apply an electric and a magnetic force to a charged particle in such a way that these forces balance. = E + = 2/2/12 14 Crossed E and ields Torque on a Current Loop We first hae to define an unambiguous direction of the loop, perpendicular to the plane of the loop nˆ. We do this with our right hand (again) This deice is called a Velocity elector. COCLUO: There is only one particular elocity of a + charged particle that will balance the magnetic and electric forces 2/2/12 15 Curl your fingers of your right hand in the direction of the current, then your thumb should point in the direction of nˆ 2/2/

5 Rectangular Current Loop in a ield Torque on a Magnetic Dipole lat current loop of arbitrary shape area of loop ˆn wants to align with : τ = absinθ = Asinθ wherea=ab and the formula does OT depend on the shape of the loop, only on the area A counts the number of turns of wire in this loop, each turn contributes. 2/2/12 17 number of turns in loop τ = µ remember an electric dipole in an E field whereτ = p E. 2/2/12 18 Magnetic Dipole in a Uniform ield τ = µ τ = µ sinθ When = o or 18 o, =. Howeer, = 18 o is unstable. When a torque is exerted through an angle, work is done. When a dipole is rotated through an angle d" dw = τ dθ = µ sinθdθ du = dw = + µ sinθdθ U = du = µ sinθ = µ cosθ + U U = Choose ( θ 9 ) = U = µ cosθ = µ 2/2/12 19 Potential Energy of Magnetic Dipole cos18 U = + µ o cos = µ 2/2/12 2 5