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.
B.
C.
D.

Explanation

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

### Step 1: Understand the Properties of Electric Field Lines
Electric field lines have specific properties:
- They start from positive charges and end at negative charges.
- They cannot cross each other.
- They cannot form closed loops or circular paths.
- In a region with no charges, the field lines should not originate or terminate.

### Step 2: Analyze Each Pattern
We will analyze each of the four patterns (A, B, C, D) based on the properties mentioned above.

#### Pattern A
- The field lines are converging and diverging simultaneously.
- This is not possible in electrostatics, as field lines cannot both converge and diverge at the same point.

**Conclusion for A:** Not a possible electrostatic field.

#### Pattern B
- The field lines appear to originate from a positive charge and terminate at a negative charge.
- There are no closed loops; the lines do not cross each other.
- This pattern can represent an electrostatic field if there are charges present outside the shown region.

**Conclusion for B:** Possible electrostatic field.

#### Pattern C
- The field lines appear to originate from nowhere, which violates the principle that field lines must start from a charge.
- Since there are no charges in the region shown, this pattern cannot represent an electrostatic field.

**Conclusion for C:** Not a possible electrostatic field.

#### Pattern D
- The field lines form a circular path.
- Electric field lines cannot form closed loops or circular paths, as they must originate from a charge and terminate at another charge.

**Conclusion for D:** Not a possible electrostatic field.

### Final Conclusion
Based on the analysis, the only pattern that represents a possible electrostatic field is **Pattern B**.

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