Parallel Plates and charge density

In summary, the electric field at the points A, B, C, and D is -2.82e4, +1.13e4, -1.69e4, and +2.26e4 volts, respectively.
  • #1
Fanman22
42
0
Three very large square planes of charge are arranged as shown (on edge) in Fig. 21-70. From left to right, the planes have charge densities per unit area of -0.50 µC/m2, +0.20 µC/m2, and -0.30 µC/m2. Find the total electric field (direction and magnitude) at the points A, B, C, and D. Assume the plates are much larger than the distance AD.

A | B | C | D

I know that the Efield= charge density/2epsilon but I'm having trouble adding the fields. For example, Point B I would think equals E of the first plate + E of the second plate (due to the positive and negative signs). My answer of 2.82e4 + 1.13e4 = 3.95e4...is this correct?

Thanks in advance for the help, it is greatly appreciated.
 
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  • #2
All plates contribute to the total field in all regions. You just need to give them the appropriate sign depending on which side of the plate you're on. Just remember the field lines of a plate point towards the plate if the charge is negative and away if it's positive.
 
  • #3
ok, but would point B, for example, be influenced by the charge density on the 3rd plate? If so, I am assuming that i should draw the diagram with arrows and add up all arrows in one direction and subtract all arrows in the opposite direction.
 
  • #4
Yes. Don't forget the superposition principle, that the total field is equal to the sum of the field contributions by all charges.
 
  • #5
I'm not sure if I'm going about this correctly. Just for your reference, Plate 1 has a E of -2.82e4, Plate 2 an E of 1.13e4, and Plate 3 an E of -1.69e4...

Let's take point B:
I am considering fields to the left to be negative and to the right to be positive.
Plate 1 will be a negative 2.82e4
Plate 2 will be a negative 1.13e4
Plate 3 will be a positive 1.69e4
add those all up and the Efield that B experiences should be -2.26e4

Is that correct?
 
  • #6
That looks right.
 
  • #7
thanks, everything came out correct.
 

Related to Parallel Plates and charge density

1. What are parallel plates?

Parallel plates refer to two flat surfaces that are in the same plane and are separated by a small distance. These plates are typically made of a conductive material such as metal and are used in various scientific experiments and devices.

2. How does charge density relate to parallel plates?

Charge density is a measure of the amount of electric charge per unit area. In the case of parallel plates, the charge density is the amount of charge on each plate divided by the area of the plates. It plays a crucial role in determining the strength of the electric field between the plates.

3. What is the electric field between parallel plates?

The electric field between parallel plates is constant and uniform, meaning it has the same magnitude and direction at all points between the plates. It is given by the equation E = σ/ε, where σ is the charge density and ε is the permittivity of the medium between the plates.

4. How does the distance between parallel plates affect the electric field?

The electric field between parallel plates is inversely proportional to the distance between the plates. This means that as the distance between the plates increases, the electric field decreases. This relationship is described by the equation E = σ/(εd), where d is the distance between the plates.

5. What are some applications of parallel plates and charge density?

Parallel plates and charge density have various applications in science and technology. They are commonly used in capacitors, which store electric charge and energy. They are also used in particle accelerators, where they are used to produce and control electric fields. Additionally, they are used in electrostatic precipitators, which remove dust and other particles from industrial exhaust gases.

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