91Ó°ÊÓ

A proton is accelerated in the direction shown by the arrow labeled \(\vec a\) in Figure 23.118. Which of the arrows labeled A–F correctly shows the direction of the vector \({\vec a_ \bot }\)at the observation location indicated by the vector \(\vec r\)?

A positive charge coasts upward at a constant velocity for a long time. Then at $\mathit{t}\mathbf{}\mathbf{=}\mathbf{}\mathbf{0}$(Figure 23.120) a force acts downward on it for $\mathbf{1}\mathbf{}\mathit{n}\mathit{s}\mathbf{}\mathbf{(}\mathbf{1}\mathbf{×}{\mathbf{10}}^{\mathbf{-}\mathbf{9}}\mathbf{}\mathbf{s}\mathbf{)}$. After this force stops acting, the charge coasts upward at a smaller constant speed for 1 ns; then a force acts upward for and it resumes its original speed. The new position reached at $\mathit{t}\mathbf{=}\mathbf{3}\mathbf{}\mathit{n}\mathit{s}$is much less than a millimeter from the original position.

You stand at location A $\mathbf{30}\mathbf{}\mathit{m}$, to the right of the charge (Figure 23.120), with instruments for measuring electric and magnetic fields. What will you observe due to the motion of the positive charge, at what times? You do not need to calculate the magnitudes of the electric and magnetic fields, but you do need to specify their directions, and the times when these fields are observed.

A slab (pulse) of electromagnetic radiation that is 15cm thick is propagating downward (in the direction) toward a short horizontal copper wire located at the origin and oriented parallel to the z axis, as shown in Figure 23.123. (a) The direction of the electric field inside the slab is out of the page (in the$\mathbf{+}\mathbf{}\mathit{z}$ direction). On a diagram, show and describe clearly the direction of the magnetic field inside the slab.

(b) You stand on the x axis at location$<12,0,0>\mathbf{}\mathit{m}$, at right angles to the direction of propagation of the pulse. Your friend stands on the z axis at location$<0,0,12>\mathbf{}\mathit{m}$. The pulse passes the copper wire at time ${\mathit{t}}_{\mathbf{1}}\mathbf{=}\mathbf{0}$, and at a later time ${\mathit{t}}_{\mathbf{2}}$ you observe new nonzero electric and magnetic fields at your location, but your friend does not. Explain. What is ${\mathit{t}}_{\mathbf{2}}$? (Give a numerical answer.) How long a time do these new fields last for you? (c) On a diagram, show and describe clearly the directions of these new nonzero fields ($\stackrel{\mathbf{→}}{\mathbf{E}}$ and $\stackrel{\mathbf{→}}{\mathbf{B}}$) at your location. Explain briefly but carefully.

A point source of green light is placed on the axis of a thin converging lens, 7cm to the left of the lens. The lens has a focal length of 10cm. Where is the location of the image of the source? Is it a real or a virtual image? If you placed a sheet of paper at the location of the image, what would you see on the paper.

You have a small but bright computer display that is only 4cm wide by 3cm tall. You will place a lens near the display to project an image of the display about 2.5m tall onto a large screen that is 6m from the lens of the projector. (a) Should you use a converging lens or a diverging lens? (b) Approximately, what should the focal length of the lens be? (c) Suppose that you choose a lens that has the focal length that you calculated in part (b). What exactly should be the distance from the computer display to the lens? (d) In order that the screen display be right side up, should the computer display be inverted or right side up? (e) On another occasion the screen is moved close, so that it is only 4m from the lens. To focus the image, you have to readjust the distance between the computer display and the lens. What is the new exact distance from the computer display to the lens? (f) How tall is the image on the screen, now that the screen is only 6m from the lens?