Physics 212 Lecture 12, Slide 1 Physics 212 Lecture 12 Magnetic Force on moving charges

Physics 212 Lecture 12, Slide 2 Magnetic Observations N S Bar Magnets Compass Needles S N N S cut in half 07 N S Magnetic Charge?

Physics 212 Lecture 12, Slide 3 Compass needle deflected by electric current I Magnetic fields created by electric currents Magnetic fields exert forces on electric currents (charges in motion) V V I I F F V V I I F F Magnetic Observations 12

Physics 212 Lecture 12, Slide 4 Magnetism & Moving Charges All observations are explained by two equations: Lorentz Force 14 Biot-Savart Law

Physics 212 Lecture 12, Slide 5 Cross Product Review Cross Product different from Dot Product –A ● B is a scalar; A x B is a vector –A ● B proportional to the component of B parallel to A –A x B proportional to the component of B perpendicular to A Definition of A x B –Magnitude: ABsin  –Direction: perpendicular to plane defined by A and B with sense given by right-hand-rule 16

Physics 212 Lecture 12, Slide 6 Remembering Directions: The Right Hand Rule x y z B F qv 17

Physics 212 Lecture 12, Slide 7 Three points are arranged in a uniform magnetic field. The B field points into the screen. 1) A positively charged particle is located at point A and is stationary. The direction of the magnetic force on the particle is: Checkpoint 1a The particle’s velocity is zero. There can be no magnetic force. 18 ABCDEABCDE

Physics 212 Lecture 12, Slide 8 Three points are arranged in a uniform magnetic field. The B field points into the screen. 1) A positively charged particle is located at point A and is stationary. The direction of the magnetic force on the particle is: ABCDEABCDE 21 X qv B F Checkpoint 1b

Physics 212 Lecture 12, Slide 9 Cross Product Practice Positive charge coming out of screen Magnetic field pointing down What is direction of force ? A) LeftB) RightC) UPD) Down E) Zero screen x y z B 24 - x + x + y - y

B field cannot change kinetic energy of a charge. No work done by B field  Kinetic energy is constant is constant But can change !

Physics 212 Lecture 12, Slide 11 x x x x x x x Uniform B into page q v F q v F q v F q v F R 30 Solve for R: Cyclotron Motion – uniform B field constant Centripetal acceleration:

Physics 212 Lecture 12, Slide 12 LHC 17 miles diameter

Physics 212 Lecture 12, Slide 13 The drawing below shows the top view of two interconnected chambers. Each chamber has a unique magnetic field. A positively charged particle is fired into chamber 1, and observed to follow the dashed path shown in the figure. Checkpoint 2a 34 qv F B. BACD

Physics 212 Lecture 12, Slide 14 The drawing below shows the top view of two interconnected chambers. Each chamber has a unique magnetic field. A positively charged particle is fired into chamber 1, and observed to follow the dashed path shown in the figure. Observation: R 2 > R 1 36 Checkpoint 2b ABCABC

Physics 212 Lecture 12, Slide 15Calculation A particle of charge q and mass m is accelerated from rest by an electric field E through a distance d and enters and exits a region containing a constant magnetic field B at the points shown. Assume q,m,E,d, and x 0 are known. What is B? –Calculate v, the velocity of the particle as it enters the magnetic field –Use Lorentz Force equation to determine the path in the field as a function of B –Apply the entrance-exit information to determine B X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X B B x 0 /2 exits here enters here d q,m x0x0 E

Physics 212 Lecture 12, Slide 16Calculation A particle of charge q and mass m is accelerated from rest by an electric field E through a distance d and enters and exits a region containing a constant magnetic field B at the points shown. Assume q,m,E,d, and x 0 are known. What is B? X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X B B x 0 /2 exits here enters here d q,m Why?? –Conservation of Energy Initial: Energy = U = qV = qEdInitial: Energy = U = qV = qEd Final: Energy = KE = ½ mv 0 2Final: Energy = KE = ½ mv 0 2 –Newton’s Laws a = F/m = qE/ma = F/m = qE/m v 0 2 = 2adv 0 2 = 2ad x0x0 E What is v 0, the speed of the particle as it enters the magnetic field ? (A) (B) (C) (D) (E)

Physics 212 Lecture 12, Slide 17Calculation A particle of charge q and mass m is accelerated from rest by an electric field E through a distance d and enters and exits a region containing a constant magnetic field B at the points shown. Assume q,m,E,d, and x 0 are known. What is B? X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X B B x 0 /2 exits here enters here d q,m Why?? –Path is circle ! Force is perpendicular to the velocityForce is perpendicular to the velocity Force produces centripetal accelerationForce produces centripetal acceleration Particle moves with uniform circular motionParticle moves with uniform circular motion x0x0 X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X What is the path of the particle as it moves through the magnetic field? (A) (B) (C) X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X E

Physics 212 Lecture 12, Slide 18Calculation A particle of charge q and mass m is accelerated from rest by an electric field E through a distance d and enters and exits a region containing a constant magnetic field B at the points shown. Assume q,m,E,d, and x 0 are known. What is B? X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X B B x 0 /2 exits here enters here d q,m Why?? x0x0 X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X R x o /2 E What is the radius of path of particle? (A) (B) (C) (D) (E)

Physics 212 Lecture 12, Slide 19Calculation A particle of charge q and mass m is accelerated from rest by an electric field E through a distance d and enters and exits a region containing a constant magnetic field B at the points shown. Assume q,m,E,d, and x 0 are known. What is B? X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X B B x 0 /2 exits here enters here d q,m Why?? x0x0 E (A) (B) (C) (D) (E)

Physics 212 Lecture 12, Slide 20Follow-Up A particle of charge q and mass m is accelerated from rest by an electric field E through a distance d and enters and exits a region containing a constant magnetic field B at the points shown. Assume q,m,E,d, and x 0 are known. What is B? X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X B B x 0 /2 exits here enters here d q,m x0x0 Suppose the charge of the particle is doubled (Q = 2q),while keeping the mass constant. How does the path of the particle change? (A) (B) (C) E Several things going on here 1. q changes  v changes 2. q & v change  F changes 3. v & F change  R changes

Physics 212 Lecture 12, Slide 21Follow-Up A particle of charge q and mass m is accelerated from rest by an electric field E through a distance d and enters and exits a region containing a constant magnetic field B at the points shown. Assume q,m,E,d, and x 0 are known. What is B? X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X B B x 0 /2 exits here enters here d q,m x0x0 Suppose the charge of the particle is doubled (Q = 2q),while keeping the mass constant. How does the path of the particle change? How does v, the new velocity at the entrance, compare to the original velocity v 0 ? Why?? E (A) (B) (C) (D) (E)

Physics 212 Lecture 12, Slide 22Follow-Up A particle of charge q and mass m is accelerated from rest by an electric field E through a distance d and enters and exits a region containing a constant magnetic field B at the points shown. Assume q,m,E,d, and x 0 are known. What is B? X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X B B x 0 /2 exits here enters here d q,m x0x0 Suppose the charge of the particle is doubled (Q = 2q),while keeping the mass constant. How does the path of the particle change? How does F, the magnitude of the new force at the entrance, compare to F 0, the magnitude of the original force? Why?? E (A) (B) (C) (D) (E)

Physics 212 Lecture 12, Slide 23Follow-Up A particle of charge q and mass m is accelerated from rest by an electric field E through a distance d and enters and exits a region containing a constant magnetic field B at the points shown. Assume q,m,E,d, and x 0 are known. What is B? X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X B B x 0 /2 exits here enters here d q,m x0x0 Suppose the charge of the particle is doubled (Q = 2q),while keeping the mass constant. How does the path of the particle change? How does R, the radius of curvature of the path, compare to R 0, the radius of curvature of the original path? Why?? E (A) (B) (C) (D) (E)

Physics 212 Lecture 12, Slide 24Follow-Up A particle of charge q and mass m is accelerated from rest by an electric field E through a distance d and enters and exits a region containing a constant magnetic field B at the points shown. Assume q,m,E,d, and x 0 are known. What is B? X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X B B x 0 /2 exits here enters here d q,m x0x0 Suppose the charge of the particle is doubled (Q = 2q),while keeping the mass constant. How does the path of the particle change? (A) (B) (C) E