This problem leads you through a study of electric and magnetic fields as viewed by two...

This problem leads you through a study of electric and magnetic fields as viewed by two different observers, that is, in two different reference frames. Suppose a charge is moving with a constant velocity (Fig. P20.94) and that its trajectory takes it to within a distance L of stationary charge . (a) What are the magnitude and direction of the resulting electric current? (b) Equation 20.19 gives the magnetic field produced by a current-carrying wire. Assume this relation can also be applied here (it can!) and use it to find the magnetic field produced by the current in part (a). What is the resulting magnetic field a distance L from the path of ? (c) Now assume charge has a velocity parallel to . Use the result from part (b) to show that the magnitude of the magnetic force on q2 when the two charges are at their closest is (d) What is the direction of the force in part (c) if and are both positive charges? If one is positive and one is negative? An observer watching and travel by would say that the force found in part (c) is a magnetic force. An observer in a moving reference frame would see things differently. If an observer is moving along with at velocity , he or she would say that is not moving, so the current and hence the magnetic field and the magnetic force are zero. However, this observer would still find that there is a force between the two charges as given in part (c) and would attribute it to an extra electric field Hint: The Coulomb’s law force produced by must be equal to the force found in part (c). This electric field is a relativistic effect, and we’ll discuss the ideas behind it in Chapter 27.