Week 7 Lorentz Force Amperes Law Faradays Law. the Lorentz force is the force on a point charge due to electromagnetic fields. It is given in terms of

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Week 7 Lorentz Force Amperes Law Faradays Law Slide 2 the Lorentz force is the force on a point charge due to electromagnetic fields. It is given in terms of the electric field E and magnetic flux density B: F = q( E + v x B) Slide 3 If a charged particle moves into a magnetic field, the particle will take on a curved trajectory: Notice that the force and the magnetic field are perpendicular to each other. This means that the B field does not do work on the charged particles or current. Slide 4 The speed is just right, the forces will cancel each other out and the charge will move in a straight line Slide 5 The radius of the trajectory is proportional to the mass-to-charge ratio This allows us to separate heavier ions from lighter ones Slide 6 Since the force constantly changes the direction of the electron, the electron will start moving in a circular pattern preserving its initial speed v o. To derive an expression for the radius of rotation r in terms of B o, set the magnitude of F equal to the centrifugal force m e r 2 Slide 7 An electron with constant velocity v = v o x enters in a magnetic field B = B o z. Calculate the initial magnetic force F exerted on the electron. Slide 8 In semiconductors, the current carriers can be either electrons or electron holes. Electron holes (or simply holes) have a positive charge. Slide 9 The forces on the charge carriers in a conductor in the presence of a magnetic field give rise to a voltage (Vab) across the width of the conductor. Slide 10 Determine which terminal of the galvanometer is positive if the material is p type. Slide 11 This law relates the magnetic flux density B to its source, the current I. Slide 12 The line integral of the magnetic flux density B over a closed contour is proportional to the net current through the surface enclosed by the contour: Notice that the double integral is evaluated over the surface S enclosed by the closed curve C. The line integral is evaluated around the closed curve C. Slide 13 The equation is correct in the special case where the electric field is constant (i.e. unchanging) in time. Otherwise, the equation must be modified. Slide 14 The direction of the line differential and the direction of the surface differential are resolved using the right-hand rule: When the index-finger of the right-hand points along the direction of line integration, the outstretched thumb points in the direction that must be chosen for the vector area da, and current passing in that same direction must be counted as positive. Slide 15 Using Amperes law, find B around a straight wire carrying a current I. Assume the wire is aligned with the z-axis. Slide 16 The magnetic flux density B in a cylindrical region 0 r a carrying a current I z is given by B = o I z r 2 a 2 Determine the surface current density J z. Slide 17 A cable consisting of an inner conductor, surrounded by a tubular insulating layer typically made from a flexible material with a high dielectric constant, all of which is then surrounded by another conductive layer (typically of fine woven wire for flexibility, or of a thin metallic foil), and then finally covered again with a thin insulating layer on the outside. The term coaxial comes from the inner conductor and the outer shield sharing the same geometric axis. Slide 18 Coaxial cables are often used as a transmission line or radio frequency signals. In a coaxial cable the electromagnetic field carrying the signal exists only in the space between the inner and outer conductors. A coaxial cable provides protection of signals from external electromagnetic interference, and effectively guides signals with low emission along the length of the cable. Slide 19 The curl of the magnetic flux density B is proportional to the current density that creates it: Again, this equation only applies in the case where the electric field is constant in time. Slide 20 The absence of B fields around a coaxial cable results in no interference in nearby electrical equipment and wires. Show that if the current is the same magnitude in each direction, the magnetic field B outside the coaxial cable is zero. Find B for a