The motion of a charged particle in an electromagnetic field can be obtained from the lorentz equation. if the electric field vector is e and the magnetic field is b, the force on a particle of mass m that carries a charge q and has a velocity v where we assume u < < c(speed of light) (a) if there is no electric field and if the particle enters the magnetic field in a direction perpendicular to the lines of magnetic flux, show that the trajectory is a circle with radius mu where wqb/m is the cyclotron frequency the yz-plane. thus show that the z component of the motion is given by (b) choose the z-axis to lie in the direction of b and let the plane containing e and b be 2m where (c) continue the calculation and obtain expressions for č(t) and y(t). show that the time averages of these velocity components are (show that the motion is periodic and then average over one complete period.) (d) integrate the velocity equations found in (c) and show (with the initial conditions cos wet + t, y(t)- sin wct. these are the parametric equations of a trochoid. sketch the projections of the tra- jectory on the xy-plane for the cases (i) a 〉 ey/bi, (ii) a < ie,/bi, and (iii) a = ie, /bi. (the last case yields a cycloid.)

Fill in the blanks with the numbers is a measure of the resistance to flow. a high liquid has a high resistance to flow and flows slowly. the ancients thought everything in the world was made of 4 we now know that there are 94 naturally occurring and scientists have created another 24 i am certain they will create even more. honey flows slowly because it has a high to flowing. a can be separated by physical means because it contains more than one pure substance and 2 pure substances are not chemically bonded to each other. a cannot be separated by physical means. all matter is made up of all elements are with the same number of protons. if it is just a single or many bonded together, if all of them have the same number of protons, it is an element. in a piece of pure iron metal, all the are joined together, that piece of iron metal is called elemental iron. a single of iron is called elemental iron. a mixture has differences from place to place. we might need a microscope to see them or they might be obvious to the unaided eye. there are surfaces separating it into different phases. a mixture is the same everywhere. it is uniform. there are no surfaces separating it into different phases. if different kinds of atoms (different elements) are bonded together by their electrons, it is called a there are physical means of to isolate the different pure substances in a mixture and there are chemical means of to isolate the different elements in a compound. 1. element 2. compound 3. mixture 4. heterogeneous 5. homogeneous 6. pure substance 7. atoms 8. separation 9. viscosity 10. resistance