A long cylindrical shell carries positive surface charge `sigma` in the upper half and negative surface charge `-sigma` in the lower half. The electric field lines around the cylinder will look like figure given in:(figures are schematic and not drawn to scale)
A
B
C
D
Text Solution
AI Generated Solution
The correct Answer is:
To solve the problem, we need to analyze the electric field created by a long cylindrical shell with a positive surface charge density \( \sigma \) on the upper half and a negative surface charge density \( -\sigma \) on the lower half.
### Step-by-Step Solution:
1. **Understanding the Charge Distribution**:
- The cylindrical shell has a positive charge density \( \sigma \) on the upper half and a negative charge density \( -\sigma \) on the lower half. This creates an electric field due to the separation of charges.
2. **Direction of Electric Field**:
- The electric field lines always point away from positive charges and towards negative charges. Therefore, for this cylindrical shell:
- The electric field lines will originate from the upper half (positive charge) and will point downwards towards the lower half (negative charge).
3. **Symmetry of the Problem**:
- The cylindrical shell is symmetrical about its axis. This symmetry implies that the electric field lines will be uniform and radial in nature, extending outward from the surface of the cylinder.
4. **Sketching the Electric Field Lines**:
- The electric field lines will start from the positive surface charge and curve downwards towards the negative surface charge.
- The lines will be denser near the surface where the charge density is higher and will spread out as they move away from the cylinder.
5. **Identifying the Correct Figure**:
- After analyzing the electric field lines, we can compare our sketch with the given options. The correct figure will show lines emanating from the upper half and curving downwards towards the lower half.
6. **Conclusion**:
- Based on the analysis, the correct option that represents the electric field lines around the cylinder is option 4.
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