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Unit 1

1.2 Electric Fields & Electric Potential

3 min readโ€ขjanuary 6, 2021

peter57616

Peter Apps


Electric Fields

Every charged object has an electric field surrounding it, similar to how every object with mass has its own gravitational field. The more charge (or mass) there is, the stronger the field is. The only difference is that while a gravitational field must be attractive, an electric field can be either attractive or repulsive. By convention, we use the direction that a positive test charge will move to draw our electric fields.
Rules for drawing:
  • Field lines are vectors and must be drawn with arrows.
  • Lines go away from a positive charge and towards a negative charge.
  • The strength of the field can be visually represented by the density of the field lines. Therefore field, lines must never touch or cross. This would represent an infinitely strong field.

Simple Fields

  • Point Charges
    • Notice the radial symmetry in the fields.
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-8pspZog1qXsC.png?alt=media&token=e5234b82-7326-48b1-bc8c-2a6c292d82c9

Image from wikimedia.org

  • Two Point Charges
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-Z6V3SUjAdT5K.1?alt=media&token=3a91c521-e8ec-4c77-9f50-f259959ba9b8

Image from Ck12.org

  • Two Parallel Plates
    • Notice how the field is the same everywhere between the plates.
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-imCG5RKGxyU3.png?alt=media&token=6e363e6e-94b1-4885-8ae6-79cabe75af41

Image from researchgate.net

Try using the PhET simulation to create your own fields and notice the how the field strength changes as a function of charge and distance.

Electric Field Strength

We've seen visually what electric fields look like. Now it's time to mathematically describe them.
The basic idea is to place a test charge at various locations in the field, measure the electrostatic force at that location, then calculate the field strength. The equation off of your reference tables for electric field strength is:
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-2KYtOZ9R0D0K.PNG?alt=media&token=da06d81d-7ee3-4fb6-9fab-549230fb3d4f
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-x1es3DPTyYzm.PNG?alt=media&token=2461434d-389e-46a5-9710-bb2cac6fadc9

Electric Fields in Conductors & Insulators

Suppose you bring a conductor near a charged object. The side of the conductor closest to the charged object will be induced with the opposite charge. However, the charge will only exist on the surface of the conductor. There will NEVER be an electric field inside a conductor. On the contrary, an insulator can store the charge inside and may have an internal electric field.
Here's an animation from Wikipedia showing how this works in a conductor. When an external electrical field (arrows) is applied, the electrons (little balls) in the metal move to the left side of the cage, giving it a negative charge. The remaining unbalanced charge of the nuclei gives the right side a positive charge. These induced charges create an opposing electric field that cancels the external electric field throughout the box. This is the basic idea behind a Faraday Cage.
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-F1EG7Wixwi7G.gif?alt=media&token=7a18a365-5fe6-48b7-9721-63a25238da88

Image from Wikipedia.org

Practice Questions

1. Ranking the strength (magnitude) of the electric force:
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-BQSGsoNmFBpu.png?alt=media&token=37d6460c-169c-4e9e-b16a-e72c4c6ee040

Answer:

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-j2TCReFf4ryp.PNG?alt=media&token=6661176c-860f-48d9-a6d1-1d27a95cf93b
2. Looking at the graph and details below, determine at which point, if any, the electric field strength is zero.
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-F8sAlSmrGdhW.png?alt=media&token=f8543ccd-2e15-4702-8b8a-3e81230705d5

Image from apclassroom.collegeboard.org

Answer:

Point A must have an electric field strength of 0. The point must be closer to the smaller charge (Q) than the larger charge (-4Q), so it can't be D or E. It must also be where the force vectors between the test charge point in the opposite direction so that the net force is 0. Therefore, it can't be point C either. Since the negative charge (-4Q) is 4x greater than the positive charge, the point must be 2x as far from the -4Q charge as it is from the Q charge.
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-EPpKohbA56AQ.PNG?alt=media&token=24381c01-9016-4233-94b1-48d58ffec008
That only leaves A as the answer. 3.
https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-RoJ8IyY5sSxa.png?alt=media&token=90ec1b18-a302-4a48-a7b3-4283cc91db52

Image from apclassroom.collegeboard.org

Answer:

Graph A is correct. At x = 2 and x = 4, the distance from the charges is 0, so the field strength must trend towards infinity. At x = 3, the repulsion from the 2 charges cancels out so the field must be 0 there.

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