6. Two point charges of opposite signs and different magnitudes are separated by a distance r as shown in the diagram below. At a point P between the charges, the electric potential is zero volts. This point is located at a distance r, from the positive charge and a distance r, from the negative charge. What is the distance r, in terms of r and the magnitude of the charges? 91 = +|91| 92 = -1921 P r1 r2 r-

59 Two charges, 4g and 5q, are pinned at two corners of a rectangle of the edges of 2a P. and 3a, as shown in figure. There are NO charges at the other corners but marked as Pi and P2. Consider two separate cases, where a third charge of q is to be brought from infinity. If the third charge, q, is located at P1 , let the potential energy of the system be Uj. If the third charge, q, is located at P2 , let the potential energy of the system be U,. 3a U1 Find the ratio - Uz 4q 2a "P2

4. Examine the charge distribution shown 9₁ +4.0 x 105 C 4.0 m 9₂-4.0 x 105℃ 3.0 m N a) What will the net force be on a third charge of q3 = -5.0x10-5C, placed at point Z? b) What will the total electric potential energy be if a third charge of q3 = -5.0x10-5C is placed at point Z?

Each part  shows one or more point charges. The charges have equal magnitudes. If a positive charge is moved from position i to position f, does the electric potential energy increase, decrease, or stay the same? Explain.