Suppose you design an apparatus in which a uniformly charged disk of radius R is to produce an electric field. The field magnitude is most important along the central perpendicular axis of the disk, at a point P at distance 2.70R from the disk (see Figure (a)). Cost analysis suggests that you switch to a ring of the same outer radius R but with inner radius R/2.70 (see Figure (b)). Assume that the ring will have the same surface charge density as the original disk. If you switch to the ring, by what part will you decrease the electric field magnitude at P? Number i Units (a) (6)

can you please ans (k)  & ( l)?

Protons are projected with an initial speed v. = 9,950 m/s into a region where a uniform electric field of magnitude E = 540 N/C is present (see figure below). The protons are to hit a target that lies a horizontal distance of %3D 1.30 mm from the point where the protons are launched. Target -R Proton beam (a) Find the two projection angles 0 that will result in a hit. (Enter the smaller angle first.) 02 = (b) Find the total duration of flight for each of the two trajectories. (Enter the smaller duration of flight first.) t = t2 = %3D IL || I|||

In part (a) of the figure an electron is shot directly away from a uniformly charged plastic sheet, at speed vs = 3.60 x 105 m/s. The sheet is nonconducting, flat, and very large. Part (b) of the figure gives the electron's vertical velocity component v versus time t until the return to the launch point. What is the sheet's surface charge density? Assume ts = 28.0 ps. (a) v (105 m/s) t (ps) (b)