Transcript Document
Physics 212 Lecture 12 Today's Concept: Magnetic Force on moving charges F qv B Physics 212 Lecture 12, Slide 1 Main Point 1 First, we introduced some observations involving forces exerted by bar magnets and between current carrying wires to indicate the existence of a new kind of phenomena in the world that we call magnetism Physics 212 Lecture 12, Slide 2 Main Point 2 Second, we made the claim that all magnetic effects can be described in terms of a magnetic field that is created by the motion of electric charges, i.e., electric currents. Physics 212 Lecture 12, Slide 3 Main Point 3 Third, these magnetic fields exert forces on electric charges that are in motion. We introduced the mathematical form for this force in terms of a cross product of vectors. In particular, the magnetic force on charge q moving with velocity v through a region containing a magnetic field B is given by qv cross B. Physics 212 Lecture 12, Slide 4 Magnetic Observations • Bar Magnets N S N S S N N S • Compass Needles N S Magnetic Charge? N 07 S cut in half N S N S Physics 212 Lecture 12, Slide 5 Magnetic Observations • 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 F F I F I I F V 12 Physics 212 Lecture 12, Slide 6 Magnetism & Moving Charges All observations are explained by two equations: F qv B 0 I ds rˆ dB 2 4 r 14 Today Next Week Physics 212 Lecture 12, Slide 7 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: ABsinq – Direction: perpendicular to plane defined by A and B with sense given by right-hand-rule 16 Physics 212 Lecture 12, Slide 8 Checkpoint 1a 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: A B C D E 18 Physics 212 Lecture 12, Slide 9 Physics 212 Lecture 12, Slide 10 Checkpoint 1b Three points are arranged in a uniform magnetic field. The B field points into the screen. A B C D E 21 1) A positively charged particle is located at point A and is stationary. The direction of the magnetic force on the particle is: Physics 212 Lecture 12, Slide 11 Physics 212 Lecture 12, Slide 12 Cross Product Practice F qv B • protons (positive charge) coming out of screen • Magnetic field pointing down • What is direction of force on POSITIVE charge? A) Left -x B) Right +x C) UP +y D) Down -y E) Zero y x B 24 z Physics 212 Lecture 12, Slide 13 Motion of Charge q in Uniform B Field • Force is perpendicular to v – Speed does not change – Uniform Circular Motion • Solve for R: F qv B F qvB x vx x x x x x q x R x x x x vx x x x x Fx x x x q F F q x x xF x x x x xv x x x x x x q x x x x xv x x Uniform B into page Demo 30 Physics 212 Lecture 12, Slide 14 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 . B 34 Physics 212 Lecture 12, Slide 15 Physics 212 Lecture 12, Slide 16 Checkpoint 2b 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 36 Physics 212 Lecture 12, Slide 17 Physics 212 Lecture 12, Slide 18 Calculation 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 q,m containing a constant magnetic field B at the points shown. Assume q,m,E,d, and x0 are known. x0/2 E d enters here What is B? exits here XXXXXXXXX X X X X X X X X X x0 XXXXXXXXX XXXXXXXXX B B • Conceptual Analysis – What do we need to know to solve this problem? (A) Lorentz ForceLaw ( F qv B qE ) (B) E field definition (C) V definition (D) Conservation of Energy/Newton’s Laws (E) All of the above Physics 212 Lecture 12, Slide 19 Physics 212 Lecture 12, Slide 20 Physics 212 Lecture 12, Slide 21