The Magnetic Force. x x x x x x. x x x x x x. x x x x x x q. q F = 0. q F. Phys 122 Lecture 17. Comment: What just happened...?

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1 The Magnetic orce Comment: I LOVE MAGNETISM q = qe + q q Comment: What just happened...? q = 0 Phys 122 Lecture 17 x x x x x x q G. Rybka

2 Magnetic Phenomenon ar magnet... two poles: N and S Like poles repel;; Unlike poles attract. Magnetic ield lines: (defined in same way as electric field lines, direction and density) S N Looks just like the electric dipole

3 Source of Magnetic ields? Answer: electric charge in motion Understanding source of field by bar magnet lies in understanding currents at atomic leel within bulk matter. Orbits of electrons about nuclei Intrinsic spin of electrons (more important effect) Comment: What is the difference between magnetic and electric fields? They seem similar, and although I understand that electric fields are created with charge distributions I don't understand how magnetic fields are generated with current

4 The Magnetic ield is defined by the magnetic force on a test charge Same approach for electric field: What is "magnetic force"? E = How is it distinguished from "electric" force? Start with some obserations: CRT deflection Empirical facts: a) magnitude: µ to elocity of q q q mag b) direction: to direction of q

5 Clicker An electron enters a region of space with speed and exits the region as shown with the same speed (magnitude). rom this information, what can we infer about the E y and z fields in the region? A. Only E y exists. Only z exists C. oth E y & z can exist y E? e -? x

Clicker An electron enters a region of space with speed and exits the region as shown with the same speed (magnitude). rom this information, what can we infer about the E y and z fields in the region?

6 Clicker An electron enters a region of space with speed and exits the region as shown with the same speed (magnitude). rom this information, what can we infer about the E y and z fields in the region? A. Only E y exists. Only z exists C. oth E y & z can exist If E y exists: orce y = q E y = ma y will accelerate charge in y direction The x elocity is unchanged. The y elocity is new Superposition: oerall speed is increasing. Therefore: NO E y possible How about z? Produces force on electron in x-y plane, perpendicular to. Therefore, z will NOT change the speed. ut it will change the direction of q. z exists in this example.

7 Lorentz orce The force on a charge q moing with elocity through a region of space with electric field E and magnetic field is gien by: = qe + q q q q = 0

8 Cross Product Reiew Cross Product different from Dot Product A is a scalar; A x is a ector A proportional to the component of parallel to A A x proportional to the component of perpendicular to A Definition of A x Magnitude: Asinθ Direction: perpendicular to plane defined by A and with sense gien by right- hand- rule

9 Remembering Directions: The Right Hand Rule = q 1. 1 st inger in direction of 2. Curl other fingers in direction of 3. Thumb points in direction of y q x z 1. Point ingers in direction of 2. Curl all fingers in direction of 3. Thumb points in direction of

10 Clicker Two protons each moe at speed toward a region of space which contains a constant field in the z direction. What is the relation between the magnitudes of the forces on the two protons in the magnetic field region? z y 1 2 X X X X X X X X X X X X x (a) 1 < 2 (b) 1 = 2 (c) 1 > 2 The magnetic force is gien by: = q = qsinθ In both cases the angle between and is 90 Therefore 1 = 2.

11 Clicker Two protons each moe at speed toward a region of space which contains a constant field in the z direction. 2 y X X X X X X X X X X X X 2What is 2x, the x-component of the force on the second proton? z x (a) 2x < 0 (b) 2x = 0 (c) 2x > 0 To determine the direction of the force, we use the right-hand rule. = q As shown in the diagram, 2x < 0.

12 Trajectory in Constant ield Suppose charge q enters field with elocity as shown below. What will be the path q follows? orce is always to elocity and. What is path? Path will be circle. will be the centripetal force needed to keep the charge in its circular orbit. Calculate R: R q

13 Radius of Circular Orbit Lorentz force: = q centripetal acc: a = R Newton's 2nd Law: 2 q R = ma Þ q = m R 2 This is momentum Þ R = m q This is an important result, with useful experimental consequences

14 ATLAS detector at CERN Radius of curature of particle tracks measures momentum

15 Project 8 Experiment at UW

16 Clicker L A proton, moing at speed, enters a region of space which contains a constant field in the z direction and is deflected as shown. Another proton, moing at 1 = 2, enters the same region of space and is deflected as shown. Compare the work done by the magnetic field W for, W 1 for 1 to deflect the protons? (a) W 1 < W (b) W 1 = W (c) W 1 > W Remember: work done W is defined as: W dx Remember: magnetic force is always perpendicular to the elocity: = q Therefore: the work done is ZERO in each case: 1 1 dx = dt = 0

17 Prelecture Reiew Question Particle A has twice the charge and 4 times the mass of particle. Suppose A and hae the same kinetic energy K and moe perpendicular to a constant magnetic field. Which particle moes in the smallest circle? Recall KE = p 2 /2m. A. Particle A moes in a smaller circle. Particle moes in a smaller circle C. Particles A and moe in circles of the same radius. 2q 4m q m KE = p A2 / 8m = p 2 / 2m à p A = 2p R = p q R A = p A / q A = 2 p / 2q = p / q R = p / q The same

18 Cross Product Practice Protons (positie charge) coming out of screen Magnetic field pointing down What is direction of force on POSITIVE charge? = q A) Left ) Right C) UP D) Down E) Zero x + x + y y y x z

19 The drawing below shows the top iew of two interconnected chambers. Each chamber has a unique magnetic field. A positiely charged particle is fired into chamber 1, and obsered to follow the dashed path shown in the figure. CheckPoint 6 q. = q

A positiely charged particle is fired into chamber 1, and obsered

20 The drawing below shows the top iew of two interconnected chambers. Each chamber has a unique magnetic field. A positiely charged particle is fired into chamber 1, and obsered to follow the dashed path shown in the figure. CheckPoint 8 Obseration: R 2 > R 1 R = m q > 1 2

Page 1. B x x x x x x x x x x x x v x x x x x x F. q F. q F = 0. Magnetic Field Lines of a bar magnet

Page 1. B x x x x x x x x x x x x v x x x x x x F. q F. q F = 0. Magnetic Field Lines of a bar magnet Magnetism The Magnetic orce = = 0 ar Magnet ar magnet... two poles: N and S Like poles repel; Unlike poles attract. Magnetic ield lines: (defined in same way as electric field lines, direction and density)