Figure 1: In all the problems below ř is a vector pointing from the origin of coordinate system toward the field point. 1. Consider an atom consisting of two electrons, cach of charge -e embedded in a sphere of uniform charge density of total charge +2e and radius R. In equilibrium, cach electron is a distance d from the center of the atom. Find the distance in terms of the other properties of the atom. The force on one of the electrons set equal to zero gives: 1a R3 F = e[- 3c0 If =0 d= R/2 (True, False) 4xco(2d)2

Write down the electrostatic force equation and define each letter and symbol in it. Then compute the force between two charged objects of X and Y coulombs respectively if they are at a distance from one another of Z meters. Show your calculations.

Solve 4,5

L/2+ L/2 Note: Figure not drawn to scale. 1. A very long, thin, nonconducting cylinder of length L is centered on the y-axis, as shown above. The cylinder has a uniform linear charge density +2.. oint. is located on the y-axis at y = c, where L >> ¢. a) Kecling.c Abh ri gle Circle GEOMETRY AND TRIGONOMETRY i. On the figure shown below, draw an arrow to indicate the direction of the electric field at point F due to the long cylinder. The arrow should start on and point away from the dot. ii. escribe the shape and location of a Gaussian surface that can be used to determine the electric field at point P due to the long cylinder. iii. Use your Gaussian surface to derive an expression for the magnitude of the electric field at point P. E press your answer in terms of 2, c, L, and physical constants, as appropriate. A==bh A = r² C = 277 =r8 Rectangular Solid Vi h Cy.inder Sphere V = r²t Sm V=² S-427² sine Rig Triangle 2+6²=c² cos@= tan= +2 BIL a b C 2x. Q b ADVANCED PLACEMENT PHYSICS C…

Question 1  Three point charges are held at the corners of an equilateral triangle as shown in the Figure below. Take Q = 4 μC and L = 6 cm. (d) What angle does the resultant force on the 3Q (due to the other two charges) make with the x-axis. Give your answer in degrees. Hint: make sure to write the units degrees next to your answer.  Diagram of equilateral triangle is attached also :)

Four equal charges (all +q) are placed on the corners of asquare with side length a. Please explain detailed steps and how you got to the answer.    a.)  Find an algebraic expression for the magnitude of theelectric force felt by the charge in the lower left-hand corner(circled) due to the other charges. b.) Make a sketch of the electric field lines associated with this charge distribution. Be sure to draw linesboth inside and outside the square.