Gauss' Law: Infinite plane with charge

In summary, the problem involves finding the distance between two equipotential surfaces with a potential difference of 100 V on an infinite plane of charge with a surface charge density of 6.8 µC/m2. Using the equation E=σ/(2ε0), the electric field is calculated to be 384170.791, and then using the equation ΔX=ΔV/E, the distance is found to be 0.2603 mm. However, the answer should be expressed in millimeters, resulting in a final answer of 0.2603 mm.
  • #1
SnakeDoc
27
1

Homework Statement


An infinite plane of charge has surface charge density 6.8 µC/m2. How far apart are the equipotential surfaces whose potentials differ by 100 V? In mm

Homework Equations


E=σ/(2ε0)

The Attempt at a Solution


So first I solved for E= 6.8e-6/(2*8.85e-12) = 384170.791

then because ΔV= E *ΔX
so
ΔX=ΔV/E

so then I substituted
ΔX = 100/ 384170.791
ΔX = .0002603

The site says that I've made a power of ten error the answer must be in mm but I'm not sure what I am doing wrong
 
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  • #2
SnakeDoc said:
ΔX = 100/ 384170.791
ΔX = .0002603

The site says that I've made a power of ten error the answer must be in mm but I'm not sure what I am doing wrong
So far you've expressed your ΔX in meters. What value did you enter for your answer in mm? How many significant figures did you provide?
 
  • #3
I entered 2.603 mm
 
  • #4
SnakeDoc said:
I entered 2.603 mm
Numerically the result looks to be good. How many significant figures do the given data support?
 
  • #5
I realized my mistake its supposed to be .2603mm I converted from Meters to millimeters improperly. Thank you.
 

Related to Gauss' Law: Infinite plane with charge

1. What is Gauss' Law?

Gauss' Law is a fundamental law in physics that relates the flow of electric field through a closed surface to the charge enclosed by that surface. It is used to calculate the electric field around a charge distribution.

2. What is an infinite plane with charge?

An infinite plane with charge is a theoretical concept used in physics to simplify calculations. It represents a plane that extends infinitely in all directions and has a uniform distribution of charge across its surface.

3. How is Gauss' Law applied to an infinite plane with charge?

In the case of an infinite plane with charge, Gauss' Law states that the electric field is constant and perpendicular to the plane at all points. This means that the electric field can be easily calculated using the surface charge density and the permittivity of free space.

4. What is surface charge density?

Surface charge density is the amount of electric charge per unit area of a surface. In the case of an infinite plane with charge, it is the total charge of the plane divided by its surface area.

5. How does the electric field behave around an infinite plane with charge?

As mentioned earlier, the electric field around an infinite plane with charge is constant and perpendicular to the plane at all points. This means that the electric field lines are parallel and evenly spaced, and the field strength does not vary with distance from the plane.

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