X and Y Components of the Electric Field at the Origin

In summary, the question asked for the values of the x and y components of the electric field at the origin in SI units. Using the formula (Ex, Ey) = -(∂V/∂x, ∂V/∂y) = -(ΔV/Δx, ΔV/Δy), the values were calculated to be Ex = -12.5 V/m and Ey = 0 V/m.
  • #1
Northbysouth
249
2

Homework Statement


Assume that you have a configuration of conductors with varying electric potentials applied to each. You make the following measurements of the values of the electric potential at different points in a two dimensional grid:

X = 0.0 cm Y = 0.0 cm V = 2.0 volts
X = 2.0 cm Y = 0.0 cm V = 2.25 volts
X = 0.0 cm Y = 2.0 cm V = 2.0 volts

What are the values of the x and y components of the electric field at the origin (Ex and Ey at (x, y) = (0,0))? Express the results in SI units.


Homework Equations





The Attempt at a Solution



I'm not sure where to begin. Any suggestions?
 
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  • #2
You can't, really. They haven't given you ANY information about the location of the conductors and their potentials. But the difference between the potential at the second point and the first should let you make an estimate of Ex and between the third and the first of Ey.
 
  • #3
The question references another question for help with this question. I'm told that:

(Ex, Ey) = -(∂V/∂x, ∂V/∂y) = -(ΔV/Δx, ΔV/Δy)

So, I calculated:

Ex = -2.25 V/ 0.02m = -112.5 V/m

Ey - 2 V/ 0.02 m = -100 V/m

I'm not sure if this makes any sense, and if it does then where does the negative come from?
 
Last edited:
  • #4
Northbysouth said:
The question references another question for help with this question. I'm told that:

(Ex, Ey) = -(∂V/∂x, ∂V/∂y) = -(ΔV/Δx, ΔV/Δy)

So, I calculated:

Ex = -2.25 V/ 0.02m = -112.5 V/m

Ey - 2 V/ 0.02 m = -100 V/m

I'm not sure if this makes any sense, and if it does then where does the negative come from?

ΔV means the DIFFERENCE between the potential at one point and another. I don't think you subtracting the potential at the two points.
 
  • #5
Ahh, yes you are correct. I shouldn't have missed that:

Ex = -(2.25V-2.V0/(0.02 m))
Ex = -12.5 V/m

Ey = -(2.0V - 2.0V/(0.02 m))
Ey = 0 V/m
 
  • #6
Northbysouth said:
Ahh, yes you are correct. I shouldn't have missed that:

Ex = -(2.25V-2.V0/(0.02 m))
Ex = -12.5 V/m

Ey = -(2.0V - 2.0V/(0.02 m))
Ey = 0 V/m

Yes, I think that's the answer they are looking for. You do know that the partial derivatives and the delta expressions aren't really equal, yes? The deltas are just an approximation to the true derivatives?
 
  • #7
Yes, my mistake; it should have been an approximation sign, not an equals sign.

Thank you for your help.
 

1. What is the definition of "X and Y components of the electric field at the origin"?

The X and Y components of the electric field at the origin refer to the two perpendicular components of the electric field vector at a specific point in space, typically measured at the origin (0,0) of a coordinate system. These components represent the direction and magnitude of the electric field at that point.

2. How are the X and Y components of the electric field at the origin calculated?

The X and Y components of the electric field can be calculated using the equations Ex = E*cos(θ) and Ey = E*sin(θ), where E is the magnitude of the electric field and θ is the angle between the electric field vector and the x-axis. These equations are based on the principles of trigonometry and vector addition.

3. What factors affect the X and Y components of the electric field at the origin?

The X and Y components of the electric field at the origin are affected by the magnitude and direction of the source charge, the distance from the source charge, and any intervening medium. Other factors that may influence these components include the shape and orientation of the charged object and the presence of other nearby charges.

4. How do the X and Y components of the electric field at the origin relate to each other?

The X and Y components of the electric field at the origin are perpendicular to each other, meaning they form a 90-degree angle. This is because the electric field vector is a vector quantity, meaning it has both magnitude and direction. The X and Y components represent different aspects of the overall electric field vector at a specific point.

5. What is the significance of understanding the X and Y components of the electric field at the origin?

Understanding the X and Y components of the electric field at the origin is crucial for analyzing and predicting the behavior of electric fields in various situations. It allows scientists and engineers to calculate the forces and movements of charged particles, design electrical circuits and devices, and study the effects of electric fields on different materials. Additionally, understanding these components helps to explain and predict the behavior of electromagnetic waves and their interaction with matter.

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