{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

But in general you can say that these equations

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

View Full Document Right Arrow Icon
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
Background image of page 7

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

View Full Document Right Arrow Icon
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
Background image of page 8
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 #
Background image of page 9

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

View Full Document Right Arrow Icon
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
Background image of page 10
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
Background image of page 11

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

View Full Document Right Arrow Icon
Clicker Question 24C-1 An electron is released from rest at point B (as shown to the right), where the potential is 0V.
Background image of page 12
Image of page 13
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}