Unit4WEBLectureNotes

# Unit4WEBLectureNotes - UCSD Physics 2B Summer Session I...

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UCSD Physics 2B Summer Session I Unit 4 Lecture Notes Chapter 29 The Magnetic Field Section 1 Introduction We begin by studying how magnetic fields affect charged particles and afterwards how magnetic fields themselves are created. Natural magnets called “Lodestones” were known centuries ago and, indeed, were used by early sailors as an aid to navigation by aligning themselves with the earth’s magnetic field. Not only did they attract certain metal objects but it was found that iron articles could be “magnetized” and would either attract or repel other such objects depending upon their orientation. A few experimental facts: 1. Magnets have two “poles” – North and South. 2. Unlike poles attract each other, like poles repel. 3. If you break a magnet, each piece becomes a new magnet with its own North and South. In other words, there are no magnetic monopoles. Recall electric field lines begin on positive and end on negative charges. But magnetic field lines never end – they loop right through. 4. The magnetic field lines of a bar magnet look similar to the electric field lines of an electric dipole but, again, the lines loop in a continuous direction. 5. Magnets attract ferromagnetic objects (iron and some other elements) but other elements, such as aluminum, are not attracted.

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Section 2 Magnetic Force on a Moving Charge Magnetic fields exert force on charged particles: 1. in proportion to the magnitude and sign of their electric charge q 2. in proportion to their velocity v – stationary charges feel no force 3. in a direction perpendicular to the velocity v and the field B q =⊗ Fv B Magnetic Force on moving charge This is a vector cross-product which can be calculated in one of two ways: Right Hand Rule First use the right-hand rule (RHR) to determine the direction of the force. Point the fingers in the direction of the velocity v and curl them towards the magnetic field B . The thumb points in the direction of the force F . The magnitude of the force is then found by the formula sin Fq v B θ = Magnitude of Cross-product where is the angle of rotation from v to B . Matrix Method The vector cross-product can be represented by the determinant of a matrix. The first row is composed of the three cardinal unit vectors, the second row by the component of the first vector and the third by the components of the second vector. In particular, we have here () ˆˆ ˆ ˆ det x y z y zz y x x x yy x xyz v v v v Bv B v B v B BBB ⊗= = + ij k vB i j k CAVEAT : The vector cross-product is NOT commutative, in fact,
EXAMPLE Imagine that you are looking at an aerial map as shown below. The magnetic field B points to the North and a particle with positive charge q is moving with velocity v to the East. What is the magnitude and direction of the force?

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Unit4WEBLectureNotes - UCSD Physics 2B Summer Session I...

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