Use the diagram to the right for the following two questions. As shown, an obser

Question

Use the diagram to the right for the following two questions. As shown, an observer in the earth frame (E) sees a stationary wire with no net charge. Electrons within the wire are moving to the right at speed u, so that there is a current I to the left. Below the wire is a positive charge q also moving to the right at a speed of v. Another observer (M) is moving to the right at a speed of v with respect to the earth frame. Earth frame 9. 17 pts.) What is the type and direction of the force, if any, on q as observed in the M frame? (a) There is an electrie force on q directed up the page. (b) There is an electric force on q directed down the page. (c) There is a magnetic force on q directed up the page (d) There is a magnetic force on q directed down the page. (e) There is no force on . 10. 17 pts.] If the charge density of positive charges measured in the E frame is Ag, what is the charge density of positive charges mensured in the M frame? (a) Ag

Explanation / Answer

9) Since the observer is moving with same velocity as that of the electrons inside the wire as well as the proton outside the wire, in reference frame of M both the electrons and proton are stationary. Thus, there is no current and hence no magnetic field due to the moving charges. The observer notices both the charges as static. Hence there will be only Coulomb force of electrostatic attraction between the electrons and proton. Since the wire contain more number of electrons, the proton will feel a net force of attraction towards the wire, i. e. directed up the page. Hence (a) is the correct option.

10) As the observer proton moves with the same velocity as that of the electrons inside the wire, it will experience that the electrons are stationary and the positive charges are moving in the opposite direction. Since the protons are in motion they experience a length contraction in the direction of the flow. Thus the observer charge will see that the net positive charge in the wire is more than the net negative charge. Hence charge density of positive charges will be more than that observed in earth's reference frame. The right option is (b)

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