Two charges of same polarity are kept fixed at a distance. What is the number of points in space where the electric field intensity due to this system is zero?

Options

A. 1, if charges are of name magnitude
B. 2, if charges are of unequal magnitude
C. 2
D. 1

Explanation

To solve the problem of finding the number of points in space where the electric field intensity due to two fixed charges of the same polarity is zero, we can follow these steps:

### Step 1: Understand the Configuration of Charges
We have two charges, \( Q_1 \) and \( Q_2 \), both of the same polarity (let's assume they are both positive). They are separated by a distance \( r \).

**Hint:** Visualize the charges on a straight line and remember that like charges repel each other.

### Step 2: Analyze the Electric Field Due to Each Charge
The electric field \( E \) due to a point charge is given by the formula:
\[ E = \frac{k \cdot |Q|}{r^2} \]
where \( k \) is Coulomb's constant, \( Q \) is the charge, and \( r \) is the distance from the charge to the point of interest.

**Hint:** The direction of the electric field due to a positive charge is always away from the charge.

### Step 3: Identify Points Where the Electric Field Could Be Zero
We need to find points in space where the electric fields due to \( Q_1 \) and \( Q_2 \) cancel each other out. Since both charges are positive, the electric fields will always point away from each charge.

**Hint:** The electric field can only be zero at points where the fields from both charges can oppose each other.

### Step 4: Consider the Regions Around the Charges
1. **Between the Charges:** There is a point between \( Q_1 \) and \( Q_2 \) where the fields from both charges could potentially cancel each other. However, since both fields point away from the charges, they cannot cancel each other in this region.

2. **Outside the Charges:** We can check the regions outside the two charges:
- To the left of \( Q_1 \)
- To the right of \( Q_2 \)

**Hint:** Check if the electric fields from both charges can oppose each other in these regions.

### Step 5: Analyze the Regions Outside the Charges
- **Left of \( Q_1 \):** Here, the electric field due to \( Q_1 \) points to the left (away from \( Q_1 \)), and the electric field due to \( Q_2 \) also points to the left (since it is farther away). Thus, the fields do not cancel.

- **Right of \( Q_2 \):** Similarly, the electric field due to \( Q_2 \) points to the right, and the electric field due to \( Q_1 \) also points to the right. Again, the fields do not cancel.

**Hint:** In both outer regions, the electric fields are in the same direction, hence they cannot cancel.

### Step 6: Conclusion
After analyzing all possible regions, we find that there is only one point where the electric field can be zero, which is not between the charges but rather outside the line joining them. However, since both charges are of the same polarity, there are no points in space where the electric field intensity is zero.

**Final Answer:** There are **zero points** in space where the electric field intensity due to this system is zero.