Solution
Let’s determine the direction of the electric field in each quadrant. The field due to an infinite plane is uniform (constant magnitude and direction).
- Plane A (+σ): Field points away from the plane (Left in Q2/Q3, Right in Q1/Q4).
- Plane B (-σ): Field points towards the plane (Down in Q1/Q2, Up in Q3/Q4).
Vector Summation:
- Q1 (Top-Right): Right + Down = $\searrow$ (South-East)
- Q2 (Top-Left): Left + Down = $\swarrow$ (South-West)
- Q3 (Bottom-Left): Left + Up = $\nwarrow$ (North-West)
- Q4 (Bottom-Right): Right + Up = $\nearrow$ (North-East)
Why Option (b) is correct and (a) is incorrect:
Since the individual fields are uniform, their resultant must also be uniform in each quadrant. This implies the field lines must be straight, parallel, and equally spaced.
- Option (b) correctly depicts these parallel, uniform field lines forming a “diamond” shape flow.
- Option (a) is incorrect because it depicts a non-uniform field, contradicting the properties of infinite charged planes.
Answer: (b)