3 min readโขjanuary 6, 2021

Peter Apps

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.

- Point Charges
- Notice the radial symmetry in the fields.

Image from __wikimedia.org__

- Two Point Charges

Image from __Ck12.org__

- Two Parallel Plates

- Notice how the field is the same everywhere between the plates.

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.

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:

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.

Image from Wikipedia.org

1. Ranking the strength (magnitude) of the electric force:

Answer:

2. Looking at the graph and details below, determine at which point, if any, the electric field strength is zero.

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.

That only leaves A as the answer.
3.

Image from apclassroom.collegeboard.org

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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