A uniform electric field E in the x-direction is produced by an appropriate charge configuration. A thin sheet of charge s per unit area is placed perpendicular to the
x-direction at x = 0. If the initial charge configuration is assumed to be undisturbed by the presence of the sheet, what is the total electric field on each side of the sheet?
Dont they add as vectors?
To determine the total electric field on each side of the sheet, we need to consider the contributions from the original charge configuration and the induced charges on the sheet.
1. Electric field due to the original charge configuration:
Since the sheet is placed at x = 0, we need to consider the electric field at x > 0 and x < 0 separately.
For x > 0:
The electric field due to the original charge configuration is the same as before the sheet was introduced. Let's assume this electric field is given by E_0.
For x < 0:
Since the original charge configuration is assumed to be undisturbed by the presence of the sheet, the electric field at x < 0 is still E_0.
2. Electric field due to the induced charges on the sheet:
When the sheet is introduced, it will induce charges on both sides of the sheet. These induced charges will generate their own electric fields.
For x > 0:
The induced charges on the sheet will create an electric field pointing in the negative x-direction. Let's denote this field as E_induced.
For x < 0:
Similarly, the induced charges on the sheet will create an electric field pointing in the positive x-direction. We can denote this field as -E_induced.
3. Total electric field on each side of the sheet:
Combining the contributions from the original charge configuration and the induced charges, we can write the total electric field as:
For x > 0:
E_total = E_0 - E_induced
For x < 0:
E_total = E_0 + E_induced
So, on each side of the sheet, the total electric field is the sum of the electric field due to the original charge configuration and the induced electric field from the charges on the sheet.