S13Phys2BaLec24C

# But in general you can say that these equations

• Notes
• 20

This preview shows pages 7–13. Sign up to view the full content.

But, in general, you can say that: These equations demonstrate that if you move with the electric field, your electric potential will decrease. Electric Potential

This preview has intentionally blurred sections. Sign up to view the full version.

Electric Potential As it turns out you can calculate all components of an electric field this way. Suppose you have a charge moving in an electric field, if you can measure the potential of the charge as it moves then you can find E with: This is how you can calculate the electric field (vector) from voltage (scalar). E x = ! " V " x E y = ! " V " y E z = ! " V " z ! E = E x ˆ i + E y ˆ j + E z ˆ k
Electric Potential Conversely, you can also calculate voltage from the electric field by integrating over a distance (two points: initial and final): This gives us the following relationships: Many times you will be asked to find one variable given the expression of one of the others, just recall how they are related. V f ! V i = ! ! E " d ! s i f #

This preview has intentionally blurred sections. Sign up to view the full version.

Electric Potential For example, in Chapter 22 we found that the electric field on the z-axis from a charged disk was: If we wanted to find the electric potential we can turn to: Evaluating the right side we get: E disk = ! 2 " o 1 ! z z 2 + R 2 " # \$ \$ % & ' ' V f ! V i = ! ! E " d ! s i f # ! E ! d ! s i f " = ! 2 " o 1 # z z 2 + R 2 \$ % & & ' ( ) ) * z " dz
Electric Potential The first term is easy, but the second term needs a u-substitution, let u = (z 2 +R 2 ) Turning back to our equation for potential: We usually define a place (like V i to be zero at infinite distance), yielding: V f ! V i = ! ! 2 " o z ! z 2 + R 2 ( ) V = ! 2 " o z 2 + R 2 ! z ( ) ! E ! d ! s i f " = ! 2 " o z # z 2 + R 2 ( ) ! E ! d ! s i f " = ! 2 " o z # z 2 + R 2 ( ) \$ z

This preview has intentionally blurred sections. Sign up to view the full version.

Clicker Question 24C-1 An electron is released from rest at point B (as shown to the right), where the potential is 0V.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern