I Electric Field Shielding by Conducting Sheets

AI Thread Summary
A thin conducting sheet does not completely shield the electric field from a point charge, as it develops a charge distribution that allows the field to reach the opposite side. The effectiveness of shielding increases with the size of the sheet, with an infinite sheet theoretically resulting in zero electric field on one side. When placed between two point charges, the conducting sheet acts as an equipotential surface, influencing the interaction between the charges. Each charge experiences a net force towards the sheet, regardless of their signs, especially when they are near the sheet and away from its edges. Grounding the sheet can further enhance the shielding effect.
NikhilRG
Messages
1
Reaction score
0
TL;DR Summary
Thin conducting sheet placed in front of a point charge.
Dear Experts,
When a thin conducting sheet with no charge on is placed at a certain distance from a point charge, does it shield the electric field caused due to the point charge from reaching the other side of the sheet. As an extension of that idea, when a conducting sheet or slab is placed in the space between two point charges in space, how will the interaction between the point charges be affected by the introduction of the conducting sheet between them.
 
Physics news on Phys.org
Hello @NikhilRG ,
:welcome: ##\qquad##!

NikhilRG said:
When a thin conducting sheet with no charge on is placed at a certain distance from a point charge, does it shield the electric field caused due to the point charge from reaching the other side of the sheet.
No it does not. A charge distribution of opposite charge will build up on the side towards the charge and that leaves the other side with a charge of the same sign.

A comparable situation is a charge within a conducting shell.

As an extension of that idea, when a conducting sheet or slab is placed in the space between two point charges in space, how will the interaction between the point charges be affected by the introduction of the conducting sheet between them.
The eletric field will be influenced because the sheet is an equipotential surface.

##\ ##
 
  • Like
Likes vanhees71 and NikhilRG
NikhilRG said:
When a thin conducting sheet with no charge on is placed at a certain distance from a point charge, does it shield the electric field caused due to the point charge from reaching the other side of the sheet.
I believe there can be significant shielding for a large sheet. The larger the sheet, the better the shielding.
1682113523821.png

The net electric field at point ##p## will be weak if ##Q## and ##p## are near the large sheet and away from the sheet edge. If the sheet is infinite, then the field will be zero at all points to the right of the sheet.

NikhilRG said:
As an extension of that idea, when a conducting sheet or slab is placed in the space between two point charges in space, how will the interaction between the point charges be affected by the introduction of the conducting sheet between them.
If the sheet is small, then it would be complicated to calculate the forces.

For a large sheet where the charges are near the sheet and away from the edge of the sheet, each charge will feel a net force toward the sheet independent of the signs of the charges.
1682113734463.png


For an infinite sheet I think we would have

$$F_1 = \frac 1 {4 \pi \epsilon_0} \frac{Q_1^2}{ (2r_1)^2} \qquad \mathrm{and} \qquad F_2 =\frac 1 {4 \pi \epsilon_0} \frac{Q_2^2}{(2r_2)^2}$$
Here, the force felt by a charge can be thought of as the attraction of the charge to its image charge. ##F_1## is independent of ##Q_2## and ##F_2## is independent of ##Q_1##.
 
  • Like
Likes SredniVashtar
Posts #2 and #3 are not conflicting: a conducting sheet definitely influences the electric field. Depending on relative size of sheet and distance between sheet and charge, there is a region where there is an amount of shielding. But the Gauss theorem (or Gauss's law) holds true in all cases.

(Which also means that the shielding is enhanced considerably by grounding the sheet!)

##\ ##
 
Last edited:
This is from Griffiths' Electrodynamics, 3rd edition, page 352. I am trying to calculate the divergence of the Maxwell stress tensor. The tensor is given as ##T_{ij} =\epsilon_0 (E_iE_j-\frac 1 2 \delta_{ij} E^2)+\frac 1 {\mu_0}(B_iB_j-\frac 1 2 \delta_{ij} B^2)##. To make things easier, I just want to focus on the part with the electrical field, i.e. I want to find the divergence of ##E_{ij}=E_iE_j-\frac 1 2 \delta_{ij}E^2##. In matrix form, this tensor should look like this...
Thread 'Applying the Gauss (1835) formula for force between 2 parallel DC currents'
Please can anyone either:- (1) point me to a derivation of the perpendicular force (Fy) between two very long parallel wires carrying steady currents utilising the formula of Gauss for the force F along the line r between 2 charges? Or alternatively (2) point out where I have gone wrong in my method? I am having problems with calculating the direction and magnitude of the force as expected from modern (Biot-Savart-Maxwell-Lorentz) formula. Here is my method and results so far:- This...
Back
Top