Consider the four field patterns shown. Assuming there are no charge in the regions shown, which of the patterns represent a possible electrostatic field?

Options

A. a.A
B. b.B
C. c.C
D. d.D

Explanation

To determine which of the four field patterns represents a possible electrostatic field, we need to analyze each option based on the properties of electric field lines. Here’s the step-by-step solution:

### Step 1: Understand the properties of electric field lines
- Electric field lines originate from positive charges and terminate at negative charges.
- Electric field lines cannot cross each other.
- Electric field lines do not form closed loops; they extend infinitely in space.

### Step 2: Analyze each option

#### Option A:
- In this option, electric field lines are shown originating and terminating at the same point.
- **Conclusion**: This is not possible because field lines cannot both originate and terminate at the same point. Therefore, **Option A is incorrect**.

#### Option B:
- In this option, the electric field lines are shown originating from a positive charge and terminating at a negative charge.
- **Conclusion**: This is consistent with the properties of electric field lines, as they can originate from a positive charge and terminate at a negative charge. Therefore, **Option B is correct**.

#### Option C:
- In this option, electric field lines are shown originating in a region where it is stated there are no charges.
- **Conclusion**: If there are no charges in the region, electric field lines cannot originate from that region. Therefore, **Option C is incorrect**.

#### Option D:
- In this option, electric field lines are shown forming a closed loop.
- **Conclusion**: Electric field lines cannot form closed paths; this is a characteristic of magnetic field lines. Therefore, **Option D is incorrect**.

### Final Conclusion:
Based on the analysis, **Option B** is the only option that represents a possible electrostatic field.

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