Lectures_Lect12

Lectures_Lect12 - Physics 212 Lecture 12 Magnetic Force on...

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Unformatted text preview: Physics 212 Lecture 12 Magnetic Force on moving charges r r r FB = qv B Physics 212 Lecture 12, Slide 1 Magnetic Observations Bar Magnets N S S N N S N S Compass Needles N S Magnetic Charge? N S 07 cut in half N S N S Physics 212 Lecture 12, Slide 2 Compass needle deflected by electric current Ma g ne tic O b s e rva tio ns I Magnetic fields created by electric currents Magnetic fields exert forces on electric currents (charges in motion) V V F F I I I F F I V V 12 Physics 212 Lecture 12, Slide 3 Magnetism & Moving Charges All observations are explained by two equations: r r r FB = qv B r r 0 I ds r ^ dB = 2 4 r Lorentz Force BiotSavart Law 14 Physics 212 Lecture 12, Slide 4 Cross Product Review Cross Product different from Dot Product A is a scalar; A x B is a vector B A proportional to the component of B parallel to A B 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 righthandrule 16 Physics 212 Lecture 12, Slide 5 Remembering Directions: The Right Hand Rule r r r FB = q v B y F qv x B z 17 Physics 212 Lecture 12, Slide 6 C h e c kp o int 1a Three points are arranged in a uniform magnetic field. The B fie ld p o ints into th e s c re e n. 1) A positively charged particle is located at point A and is stationary. The direction of the magnetic force on the particle is: A B C D E r r r F = qv B The particle's velocity is zero. There can be no magnetic force. 18 Physics 212 Lecture 12, Slide 7 Checkpoint 1b Three points are arranged in a uniform magnetic field. The B fie ld p o ints into th e s c re e n. A B C D E 1) A positively charged particle is located at point A and is stationary. The direction of the magnetic force on the particle is: r r r F = qv B qv X F 21 B Physics 212 Lecture 12, Slide 8 Positive charge coming out of screen Magnetic field pointing down What is direction of force ? A) Left B) Right x + x C) UP Cross Product Practice r r r F = qv B + y D) Down E) Zero y y x B 24 n ee scr z Physics 212 Lecture 12, Slide 9 B field cannot change kinetic energy of a charge. r r r r r FB = q v FB v B r r r r dWB = FB = FB dt = 0 dr v r FB r v No work done by B field Kinetic energy is constant r v is constant r But v can change ! Cyclotron Motion uniform B field r r r F = qv B F = qvB r v = v constant v Centripetal acceleration: a = R S o lve fo r R : 2 x x x x q vx x x F Rx q x x F x x x x x q v x x x x x x x x x x x x x xF x xF x x q v x x x x x x Uniform B into page xv x x v2 qvB = m R 30 mv R= qB Physics 212 Lecture 12, Slide 11 R= mv p = qB qB LHC 17 miles diameter Physics 212 Lecture 12, Slide 12 Checkpoint 2a 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. A B C D r r r F = qv B qv B 34 . F 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 2b A B C Observation: R2 > R1 R= 36 mv qB B1 > B2 Physics 212 Lecture 12, Slide 14 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. q,m Assume q,m,E,d, and x0 are known. What is B? Calculation x0/2 exits here XXXXXXXXX X X X X X X X X X x0 XXXXXXXXX d XXXXXXXXX enters here B B E 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 entranceexit information to determine B Physics 212 Lecture 12, Slide 15 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. q,m Assume q,m,E,d, and x0 are known. What is B? Calculation x0/2 exits here XXXXXXXXX X X X X X X X X X x0 XXXXXXXXX d XXXXXXXXX enters here B B E What is v0, the speed of the particle as it enters the magnetic field ? vo = 2qE 2E 2qEd vo = vo = 2ad vo = md m m (A) (B) (C) (D) (E) vo = qEd m Why?? Conservation of Energy Newton's Laws Initial: Energy = U = qV = qEd Final: Energy = KE = mv02 a = F/m = qE/m v02 = 2ad 2 vo = 2 1 mv2 o 2 = qEd vo = 2qEd m vo = 2qEd m qE d m Physics 212 Lecture 12, Slide 16 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. q,m Assume q,m,E,d, and x0 are known. What is B? vo = 2qEd m Calculation x0/2 exits here XXXXXXXXX X X X X X X X X X x0 XXXXXXXXX d XXXXXXXXX enters here B B E What is the path of the particle as it moves through the magnetic field? XXXXXXXXX XXXXXXXXX XXXXXXXXX XXXXXXXXX XXXXXXXXX XXXXXXXXX XXXXX XXXXXXXXX (A) (B) (C) X X X X XXXXXXXXX XXXXXXXXX XXXXXXXXX XXXXXXXXX Why?? Path is circle ! Force is perpendicular to the velocity Force produces centripetal acceleration Particle moves with uniform circular motion Physics 212 Lecture 12, Slide 17 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. q,m Assume q,m,E,d, and x0 are known. What is B? vo = 2qEd m Calculation x0/2 exits here XXXXXXXXX X X X X X X X X X x0 XXXXXXXXX d XXXXXXXXX enters here B B E What is the radius of path of particle? R = xo Why?? R R = 2 xo 1 R = xo 2 mvo R= qB 2 vo R= a (A) (B) (C) (D) (E) xo/2 XXXXXXXXX XXXXXXXXX XXXXXXXXX XXXXXXXXX Physics 212 Lecture 12, Slide 18 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. q,m Assume q,m,E,d, and x0 are known. What is B? vo = 2qEd m Calculation x0/2 exits here R = 1 x0 2 m B=E 2qEd XXXXXXXXX X X X X X X X X X x0 XXXXXXXXX d XXXXXXXXX enters here B B E 2 B= xo 2mEd q E B= v 1 B= xo 2mEd q B= mvo qxo (A) (B) (C) (D) (E) Why?? r r F = ma 2 vo qvo B = m R m vo B= q R m 2 B= q xo B= 2 xo 2qEd m 2mEd q Physics 212 Lecture 12, Slide 19 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. q,m Assume q,m,E,d, and x0 are known. What is B? FollowUp x0/2 exits here B= 2 xo 2mEd q XXXXXXXXX X X X X X X X X X x0 XXXXXXXXX d XXXXXXXXX enters here B B E 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) Several things going on here X X X X X X X X X XX 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 XX 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 XX X X X X X X X X X X X X X X X X X X X X X X X X XX X X X X X X X X X X X X X X X X 1. q changes v changes 2. q & v change F changes 3. v & F change R changes Physics 212 Lecture 12, Slide 20 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. q,m Assume q,m,E,d, and x0 are known. What is B? B= 2 xo 2mEd q FollowUp x0/2 exits here XXXXXXXXX X X X X X X X X X x0 XXXXXXXXX d XXXXXXXXX enters here B B E 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 v0? vo v v= (A) (B) (C) (D) (E) v = 2vo v = vo v= o 2 2 Why?? 1 mv 2 2 2 = QEd = 2qEd = 2 1 mvo 2 v = 2vo 2 v 2 = 2vo v = 2vo Physics 212 Lecture 12, Slide 21 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. q,m Assume q,m,E,d, and x0 are known. What is B? B= 2 xo 2mEd q FollowUp x0/2 exits here XXXXXXXXX X X X X X X X X X x0 XXXXXXXXX d XXXXXXXXX enters here B B E Suppose the charge of the particle is doubled (Q = 2q),while keeping the mass constant. How does the path of the particle change? v = 2vo How does F, the magnitude of the new force at the entrance, compare to F0, the magnitude of the original force? F = Fo (A) (B) (C) (D) (E) F = 2 Fo F= o F 2 F = 2 Fo F = 2 2 Fo Why?? F = QvB = 2q 2vo B F = 2 2 Fo Physics 212 Lecture 12, Slide 22 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. q,m Assume q,m,E,d, and x0 are known. What is B? B= 2 xo 2mEd q FollowUp x0/2 exits here XXXXXXXXX X X X X X X X X X x0 XXXXXXXXX d XXXXXXXXX enters here B B E Suppose the charge of the particle is doubled (Q = 2q),while keeping the mass constant. How does the path of the particle change? v = 2vo F = 2 2 Fo How does R, the radius of curvature of the path, compare to R0, the radius of curvature of the original path? R R R = Ro (A) (B) (C) (D) (E) R= o R= o 2 2 R = 2 Ro R = 2 Ro Why?? v2 F =m R v2 R=m F 2 2 2vo vo R R=m =m = o 2 2 Fo 2 Fo 2 Physics 212 Lecture 12, Slide 23 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. q,m Assume q,m,E,d, and x0 are known. What is B? B= 2 xo 2mEd q FollowUp x0/2 exits here XXXXXXXXX X X X X X X X X X x0 XXXXXXXXX d XXXXXXXXX enters here B B E 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) X X X X X X X X X XX 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 XX 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 XX X X X X X X X X X X X X X X X X X X X X X X X X XX X X X X X X X X X X X X X X X X Ro R= 2 A C h e c k: (Exe rc is e fo r S tud e nt) G ive n o ur re s ult fo r B (a b o ve ) , c a n yo u s h o w: R= 1 2mEd B Q R R= o 2 Physics 212 Lecture 12, Slide 24 ...
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This document was uploaded on 03/08/2012.

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