# Solving Laplace's Eqn: Setting Zero of Potential

by bcjochim07
Tags: laplace, potential, setting, solving
 Share this thread:
 P: 374 1. The problem statement, all variables and given/known data I have two quick related questions that I think will help clear something up for me. (1) An uncharged metal sphere of radius R is placed in an otherwise uniform electric field E = E0 zhat. The field induces charge. Find the potential in the region outside the sphere. (2) Find the potential outside an infitely long metal pipe of radius R placed at right angle to an otherwise uniform electric field E0. 2. Relevant equations 3. The attempt at a solution Okay, so I am mostly comfortable with the solutions to these problems, with the exception of one key concept. Problem 1: If E=E0 zhat (for r>>R, then V for r>>R is -E0z + C) The one hang-up I have is that for problem (1), you set V=0 on the xy-plane "by symmetry." Thus we can say C=0. I'm not sure I understand the reasoning behind setting V=0 for all z=0. Similarly, from problem (2), if we suppose that the electric field is pointing along z direction, so again, the form of the potential is -E0z + C. Again, one should set V=0 on the xy-plane, so C=0. I don't have a clear picture in my head of why you set V=0 on the xy-plane. Any explanations of this concept would be greatly appreciated
 Sci Advisor HW Helper PF Gold P: 2,602 Since the electric field is the gradient of the potential, $$\vec{E} = - \nabla V$$ (for electrostatics), a constant shift in the potential $$V' = V + c$$ doesn't change the electric field. Therefore we are usually free to define the location of $$V=0$$ by adding a constant term to the potential. In your examples, choosing $$V(z=0) = 0$$ is just the most convenient choice, but it was not the only one.

 Related Discussions Calculus & Beyond Homework 5 Calculus & Beyond Homework 12 Calculus & Beyond Homework 2 Differential Equations 6 Calculus & Beyond Homework 3