Lectures_Lect12

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

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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 ...
View Full Document

## This document was uploaded on 03/08/2012.

Ask a homework question - tutors are online