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Physics I Class 24 Magnetic Force on Moving Charges 24-1 Hendrick Antoon Lorentz Hendrick A. Lorentz was a Dutch physicist who refined certain aspects of electromagnetic theory. He, along with Irish mathematical physicist George F. FitzGerald, deduced fundamental properties of the electromagnetic behavior of moving bodies that formed the basis of Einstein’s Special Theory of Relativity. The force of a magnetic field on a moving charge is sometimes called the Lorentz Force. H.A. Lorentz 1853-1928 24-2 Important Facts About Velocity and Acceleration Vectors (Review) v a v Same direction: speeding up. a v a Opposite directions: slowing down. Right angles: changing direction, same speed. 24-3 Vector Cross Product (Review) c a b ; | c | | a || b | sin( ) The direction comes from the right-hand rule. It is at a right angle to the plane formed by a and b . In other words, the cross productis at right angles to both a and b . (3D thinking required!) 24-4 Drawing 3D Vectors in 2D Y -Y +Y +X -X -Z X Z +Z +Z is out of page 24-5 Magnetic Force on a Moving Charge F q vB charge of the particle (C; + or –) v : velocity of the particle (m/s) B : magnetic field (T) q: Force is at a right angle to velocity. Force is at a right angle to magnetic field. Important: If q is negative, that reverses the direction of force. 24-6 An Example An Electron in a Magnetic Field Y X Z 24-7 Analysis of the Magnetic Force Y X F q vB Z F We will evaluate this expression before the electron starts turning. First, evaluate v B . In this case, they are 90° apart, so all we need is the direction. v is +X, B is –Z, so v B is +Y. Next, we need to account for q. This is an electron, so q is negative. Therefore, the magnitude of the force is (e v B) and the direction is –Y. 24-8 Uniform Circular Motion As the electron turns, so does the force vector. Speed stays constant because acceleration is always perpendicular to velocity. The electron travels in a circle at a constant speed. 24-9 The Radius of the Circle F r v Although the directions of the vectors are changing, the magnitudes stay the same. v2 F ma m r F qvB v2 qvB m r v2 mv rm qvB qB 24-10 The Period and Frequency F r v The circumference of the circle is 2 r. Distance 2 r Time T mv 2 2r qB 2m T v v qB v f 1 qB T 2m 2f qB m 24-11 Bubble Chamber The red and green lines in the figure to the left are tracks of charged particles in a bubble chamber. Each charged particle makes a trail of tiny bubbles as it moves in the chamber. There is a magnetic field of 1.0 T directed into the page. mv r qB What are the signs of the charges of the particles? Why do they spiral inward? What are they? What created them at the points where the tracks start? 24-12 The Aurora There is no acceleration in the direction of the magnetic field line. (Why?) The component of velocity in the direction of the field line remains constant. (Why?) The component of velocity at a right angle to the field line continually changes direction. (Why?) The result is that the charged particle (electron) travels in a spiral path along the magnetic field line, giving off light when it hits the atmosphere. 24-13 The Aurora As Seen from the Space Shuttle 24-14 Class #24 Take-Away Concepts 1. The Lorentz (magnetic) force on a moving, charged particle: F q vB 2. The Lorentz force cannot change a particle’s speed, only the direction of its velocity. 3. Radius and angular frequency of a charged particle in uniform circular motion in a magnetic field: mv r qB qB m 24-15 Activity #24 Introduction to Magnetic Fields Objective of the Activity: 1. 2. Consider the implications of the Lorentz force on speed and direction of a charged particle. Determine the direction and magnitude of the magnetic field at your table in the classroom using a compass, a coil of wire, a power supply, and a current meter. 24-16