Physics 5C - Problem Set 2 Due Monday, April 15 at 11:59 PM on Gradescope UCLA / Spring 2024 / Brian Naranjo Problem 2.1 Point charges + and q are located along the z-axis at z = d/2 and = d/2, respectively. We say that the dipole is aligned in the positive z direction. In this problem, we calculate an approximation for the electric potential at point P. a) Use the law of cosines to find an expression for r2 in terms of r, 8, and d b) Use the binomial approximation to show that, for r >> d, 1 1 dcosf _ e + Ty T 272 You may drop the term proportional to (d/r)?, which will be very small. c) Repeat parts a and b for r_, showing 1 1 dcosb T T 2r? d) Finally, use our expressions for 1/r, and 1/r_ to show that the approximate electric potential at point P is __ pcosf " drmeyr?' where, as usual, p = qd. Problem 2.2 There is an ideal dipole located at the origin and aligned along the positive y direction. By \"ideal,\" we mean that it is described exactly by the electric potential _ pcost " 4mepr?' Note that, in this problem, & is measured with respect to the y-axis. A particle of charge > 0 and mass m is initially located on the y-axis at y = yo > 0. Its initial speed is vg. It is initially headed in an arbitrary direction, but it is observed that, after some time, it crosses the r-axis. What is the particle's speed when it crosses the z-axis? 2-1