AT Cycle 18

Then, THINK ABOUT THIS:  If you can calculate V by integrating E, can't you find E by taking the derivative of V?  Kind of, but the problem is that E is a vector, so how do we get a vector from a scalar?  First, for a conceptual explanation, check out the video below.  Then, read section 24-6 on page 701-702 in your textbook, and work through Sample Problem 24.05.  For some good practice, you may want to derive the expression for the electric potential at any point on the central axis of a uniformly charged disk.  Additionally, make sure to think about why Ex and Ey are zero.  Using the gradient method  E=-∇V  is a cool different way of finding the electric field.  In a lot of ways it's easier than the electric field integral, since you don't have to ever deal with component geometry.  Check it out in this video:

Finally, we'll review the concept of a contour map in hiking and relate that to getting the electric field with the gradient of the potential  E=-∇V .  We'll do an example together.  

To think about the whole unit, here are the topics in electrostatics we have studied:

• Coulomb's Law

• Finding electric field

  • E = F/q

  • electric field integral (superposition of dq)

  • Gauss's Law

• Electric potential energy of a configuration of charges

• Finding electric potential

  • potential integral (superposition of dq)

  • Path integral if we know electric field (compatible with Gauss's Law)

• Calculating field and potential due to non-uniform charge distributions (integrals)