Two charged thin infinite plane sheets of uniform surface charge density `sigma_(+) and sigma_(-)` where `|sigma_+| gt|sigma_(-)|` , intersect right angle Which of the following best represents the electric field lines for this system:

Options

A.
B.
C.
D.

Answer

To solve the problem of determining the electric field lines produced by two intersecting infinite plane sheets with uniform surface charge densities \(\sigma_+\) and \(\sigma_-\), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Configuration**:
- We have two infinite plane sheets that intersect at right angles.
- One sheet has a positive surface charge density \(\sigma_+\) and the other has a negative surface charge density \(\sigma_-\).
- It is given that \(|\sigma_+| > |\sigma_-|\).

2. **Determine the Electric Field Due to Each Sheet**:
- The electric field due to an infinite plane sheet with surface charge density \(\sigma\) is given by the formula:
\[ E = \frac{\sigma}{2\epsilon_0} \]
where \(\epsilon_0\) is the permittivity of free space.
- For the positively charged sheet (\(\sigma_+\)), the electric field points away from the sheet.
- For the negatively charged sheet (\(\sigma_-\)), the electric field points towards the sheet.

3. **Calculate the Net Electric Field**:
- Since the sheets are intersecting at right angles, we can analyze the electric fields in two perpendicular directions (let's assume the positive sheet is along the y-axis and the negative sheet is along the x-axis).
- The electric field due to the positive sheet (\(E_+\)) will be directed in the positive y-direction and has a magnitude of:
\[ E_+ = \frac{\sigma_+}{2\epsilon_0} \]
- The electric field due to the negative sheet (\(E_-\)) will be directed in the negative x-direction and has a magnitude of:
\[ E_- = \frac{\sigma_-}{2\epsilon_0} \]

4. **Analyze the Direction and Magnitude**:
- Since \(|\sigma_+| > |\sigma_-|\), the net electric field will be stronger in the direction of the positive sheet (y-direction) compared to the negative sheet (x-direction).
- Therefore, the electric field lines will be denser in the y-direction and sparser in the x-direction.

5. **Sketch the Electric Field Lines**:
- Draw the electric field lines originating from the positive sheet and terminating at the negative sheet.
- The lines will be more concentrated in the y-direction due to the greater magnitude of the electric field from the positive sheet.

6. **Select the Correct Representation**:
- Based on the analysis, the option that shows electric field lines more concentrated in the y-direction and less in the x-direction represents the correct configuration.

### Conclusion:
The correct representation of the electric field lines for the given system is the option that shows denser lines in the y-direction and sparser lines in the x-direction.