Physics 1202: Lecture 10 Today’s Agenda Announcements: –Lectures posted on: –HW assignments, solutions etc. Homework #3:Homework #3: –On Masterphysics today: due Friday this week –Go to masteringphysics.com Midterm 1: –Friday Oct. 2 –Chaps. 15, 16 & 17.

Bar Magnet Bar magnet... two poles: N and S Like poles repel; Unlike poles attract. Magnetic Field lines: (defined in same way as electric field lines, direction and density) Does this remind you of a similar case in electrostatics? You can see this field by bringing a magnet near a sheet covered with iron filings

Forces due to Magnetic Fields? Electrically charged particles come under various sorts of forces. As we have already seen, an electric field provides a force to a charged particle, F = qE. Magnets exert forces on other magnets. Also, a magnetic field provides a force to a charged particle, but this force is in a direction perpendicular to the direction of the magnetic field.

Definition of Magnetic Field Magnetic field B is defined operationally by the magnetic force on a test charge. (We did this to talk about the electric field too) What is "magnetic force"? How is it distinguished from "electric" force? Start with some observations: Empirical facts: a) magnitude:  to velocity of q b) direction:  to direction of q q F v mag

Lorentz Force The force F on a charge q moving with velocity v through a region of space with electric field E and magnetic field B is given by: F x x x v B q  v B q F = 0  v B q F  Units: 1 T (tesla) = 1 N / Am 1G (gauss) = T

Lecture 10, ACT 1 Two protons each move at speed v (as shown in the diagram) toward a region of space which contains a constant B field in the -y-direction. –What is the relation between the magnitudes of the forces on the two protons? (a) F 1 < F 2 (b) F 1 = F 2 (c) F 1 > F 2 1A B x y z 1 2 v v

Circular motion Force is perp. to v  = 90 o so sin  = 1 or F=qvB W=0   K=0 –Kinetic energy not changed –Velocity constant: UCM ! R Work proportional to cos  (recall 1201) –  :angle between F and  x –cos  =0 (perpendicular)

Lecture 10, ACT 2 Cosmic rays (atomic nuclei stripped bare of their electrons) would continuously bombard Earth’s surface if most of them were not deflected by Earth’s magnetic field. Given that Earth is, to an excellent approximation, a magnetic dipole, the intensity of cosmic rays bombarding its surface is greatest at the (The rays approach the earth radially from all directions). A) PolesB) EquatorC) Mid-lattitudes

Trajectory in Constant B Field F F v R x x x v B q Suppose charge q enters B field with velocity v as shown below. (v  B) What will be the path q follows? Force is always  to velocity and B. What is path? –Path will be circle. F will be the centripetal force needed to keep the charge in its circular orbit. Calculate R:

Radius of Circular Orbit Lorentz force: centripetal acc: Newton's 2nd Law: x x x v F B q F v R This is an important result, with useful experimental consequences !  

Ratio of charge to mass for an electron e-e- 3) Calculate B … next week; for now consider it a measurement 4) Rearrange in terms of measured values, V, R and B 1) Turn on electron ‘gun’ VV ‘gun’ 2) Turn on magnetic field B R & 

Lawrence's Insight "R cancels R" We just derived the radius of curvature of the trajectory of a charged particle in a constant magnetic field. E.O. Lawrence realized in 1929 an important feature of this equation which became the basis for his invention of the cyclotron. R does indeed cancel R in above eqn. So What?? –The angular velocity is independent of R!! –Therefore the time for one revolution is independent of the particle's energy! –We can write for the period, T=2  /  or T = 2  m/qB –This is the basis for building a cyclotron. Rewrite in terms of angular velocity  !   

The Hall Effect c d l a c B B I I - vdvd F Hall voltage generated across the conductor qE H Force balance Using the relation between drift velocity and current we can write:

Magnetic Force on a Current Consider a current-carrying wire in the presence of a magnetic field B. There will be a force on each of the charges moving in the wire. What will be the total force  F on a length  l of the wire? Suppose current is made up of n charges/volume each carrying charge q and moving with velocity v through a wire of cross- section A. N S Simpler: For a straight length of wire L carrying a current I, the force on it is: Force on each charge = Total force =  Current = or

Lecture 10, ACT 3 A current I flows in a wire which is formed in the shape of an isosceles triangle as shown. A constant magnetic field exists in the -z direction. –What is F y, net force on the wire in the y- direction? (a) F y < 0 (b) F y = 0 (c) F y > 0 x y