Calculating Electric Field at Point P above Infinite Sheet

In summary, the electric field at point P is the sum of the E field due to the sheet with positive surface charge density and the E field due to the imaginary disk with negative surface charge density. Adding the two together, the resulting value should be smaller than the E field due to the sheet alone. It may be helpful to check your calculations with a mathematical tool like WolframAlpha or Matlab.
  • #1
kopinator
41
1
What is the electric field at a point P, a distance h = 29.9 cm above an infinite sheet of charge, with a charge distribution of 2.29 C/m^2 and a hole of radius r = 4.49 cm with P directly above the center of the hole, as shown in the figure?

Equations used:
Edisk= (-σ/2ε)[1-(z/sqrt(z^2 + r^2))]
Esheet= +σ/2ε
Enet= ƩE

I converted all the cm into m and plugged the numbers in. I got 3.64e10 N/C for the disk and 1.30e11 N/C for the sheet. I added the two together but my answer was wrong so i tried subtracting and still didn't get the right answer. I thought adding them would've been correct. Am I missing something?
 
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  • #2
kopinator said:
What is the electric field at a point P, a distance h = 29.9 cm above an infinite sheet of charge, with a charge distribution of 2.29 C/m^2 and a hole of radius r = 4.49 cm with P directly above the center of the hole, as shown in the figure?

Equations used:
Edisk= (-σ/2ε)[1-(z/sqrt(z^2 + r^2))]
Esheet= +σ/2ε
Enet= ƩE

I converted all the cm into m and plugged the numbers in. I got 3.64e10 N/C for the disk and 1.30e11 N/C for the sheet. I added the two together but my answer was wrong so i tried subtracting and still didn't get the right answer. I thought adding them would've been correct. Am I missing something?

Yes, adding your expressions together is correct. You are essentially considering the E field at the point P due to the sheet with surface charge density +σ and subtracting the E field due to the imaginary disk of negative surface charge density -σ.

Alternatively, just subtract the E field due to a disk from the E field due to the plane.
In your end expression, take the limit z>>R, and see if your result makes sense.
 
  • #3
Disk and sheet should have opposite signs (as removing stuff from a sheet reduces the electric field), so your formulas look right and one of your resulting values should have a minus sign. Add both, and you get a value smaller than for the sheet alone.

Did you check your values with WolframAlpha, Matlab or something similar?
 

What is the equation for calculating electric field at a point above an infinite sheet?

The equation for calculating the electric field at a point P above an infinite sheet is E = σ/2ε₀, where σ is the surface charge density of the sheet and ε₀ is the permittivity of free space.

What is the direction of the electric field above an infinite sheet?

The electric field above an infinite sheet is always perpendicular to the sheet, pointing away from the sheet if the sheet has a positive charge density, and towards the sheet if the sheet has a negative charge density.

How does the distance from the sheet affect the magnitude of the electric field at point P?

The magnitude of the electric field at point P is inversely proportional to the distance from the sheet. This means that as the distance increases, the magnitude of the electric field decreases.

Can the electric field at point P ever be zero?

Yes, the electric field at point P can be zero if the sheet has a charge density of zero or if point P is located at an infinite distance from the sheet.

Is the electric field above an infinite sheet affected by the size or shape of the sheet?

No, the electric field above an infinite sheet is not affected by the size or shape of the sheet, as long as the sheet is infinite. This is because the sheet is assumed to have an infinite length and width, so no matter how far away point P is, the sheet will still appear to be infinite.

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