Plate A Plate B R .S .N 1. Two conducting plates, A and B, are connected to opposite sides of a battery of potential difference V and are separated by a distance d. Assume that the area of the plates is very large such that the plate dimensions are large compared to the separation distance d. Points L and T are midway between the plates, points S and R are the same horizontal distance from point T, and point R is directly above point 5. Edge effects at the points R, S, T, L, and N can be neglected. (a) What is the direction of the electric field, if any, at each of the points S, T, and N? If the electric field is zero at any of the indicated points, write "0 at the point _." (b) Rank the magnitude of the electric potential differences AVRs, AVRT, and AVAL between the pairs of points indicated by the subscripts. Use "VAS," "VAT," and "VRI" to indicate the given potential differences, respectively. If any of the quantities are equal, clearly indicate this. Justify your ranking by citing relevant physics principles.(c) While the plates remain connected to the battery, the area of each plate is doubled. Does the electric field at point 5 increase, decrease, or remain the same compared to the electric field at point S in the initial situation? Justify your answer. Plate A m. 9 plate B 1 Note: Figure not drawn to scale. The plates are returned to their original areas. The battery provides a constant potential difference V. A small charged particle of mass m has a magnitude of charge q. The particle is moving with constant speed v, as shown, when it enters the region midway between plates A and B. The particle strikes plate A at a distance y from the top of plate A. Assume gravitational forces on the particle are negligible. (d) Does the particle have a positive charge, negative charge, or no net charge? Justify your answer.A student derives the following correct relationship to describe the motion of the particle between the plates: qV (e) If the magnitude of the particle's charge is decreased, will y increase, decrease, or remain the same? Support your claim by referencing the equation above. (f) By citing relevant physics principles, explain how decreasing the charge has the effect on y that you determined in part (e). 2. A solid conducting sphere of radius a has a net charge of +Q. It is enclosed by a thin conducting spherical shell of radius b. The space between the spheres is filled with an insulating material of dielectric constant k. The thin spherical shell is then grounded briefly so that a net charge of -Q accumulates on its surface, then the ground is disconnected. A cross section of the final configuration of the spheres is shown below. K Q HG b(a) Use Gauss's Law to determine the electric field as a function of r, the distance from the center of both spheres, for the region a