When two point charges `q_(A)` and `q_(B)` are placed at some separation on positive x-axis at points `(x_(A), 0)` and `(x_(B), 0)`. Given that `|q_(A)|` and `|q_(B)|` and `x_(B) gt x_(A)`. If null point is the point where net electric field due to both the charges is zero, then

Options

A. if both `q_(A)` and `q_(B)` are positive, null point lies at some point `x_(A) lt x lt x_(B)`
B. if `q_(A)` is positive and `q_(B)` is negative, null point lies at some point `x lt x_(A)`
C. if `q_(A)` is positive and `q_(B)` is negative, null point lies at some point `x gt x_(B)`
D. if `q_(A)` is negative and `q_(B)` is positive, null point lies at some point `x gt x_(B)`

Answer

To solve the problem of finding the null point where the net electric field due to two point charges \( q_A \) and \( q_B \) is zero, we can follow these steps:

### Step 1: Understand the Configuration
We have two point charges:
- Charge \( q_A \) is located at position \( (x_A, 0) \)
- Charge \( q_B \) is located at position \( (x_B, 0) \)
- It is given that \( |q_A| > |q_B| \) and \( x_B > x_A \).

### Step 2: Determine the Regions for Electric Field
The electric field due to a positive charge points away from the charge, while the electric field due to a negative charge points towards the charge. We can analyze the electric field in three regions:
1. To the left of \( q_A \) (Region 1)
2. Between \( q_A \) and \( q_B \) (Region 2)
3. To the right of \( q_B \) (Region 3)

### Step 3: Analyze Electric Field Directions
1. **Region 1 (Left of \( q_A \))**:
- Both electric fields due to \( q_A \) and \( q_B \) point to the right (away from both charges if they are positive).
- The net electric field cannot be zero here.

2. **Region 2 (Between \( q_A \) and \( q_B \))**:
- The electric field due to \( q_A \) points to the right (away from \( q_A \)).
- The electric field due to \( q_B \) points to the left (away from \( q_B \)).
- Since \( |q_A| > |q_B| \), the electric field due to \( q_A \) will dominate. Therefore, the net electric field cannot be zero here.

3. **Region 3 (Right of \( q_B \))**:
- The electric field due to \( q_A \) points to the right.
- The electric field due to \( q_B \) also points to the right.
- The net electric field cannot be zero here either.

### Step 4: Identify the Null Point
Since the null point must be located where the electric fields from both charges are equal in magnitude and opposite in direction, we conclude that:
- The null point must lie in Region 2, between \( q_A \) and \( q_B \), closer to the smaller charge \( q_B \).

### Step 5: Conclusion
Thus, the null point lies between \( x_A \) and \( x_B \), specifically closer to \( q_B \).

### Summary of Findings
- The null point exists between the two charges.
- It is closer to the charge with the smaller magnitude, which is \( q_B \).