Two unequal and opposite charges are kept fixed at a distance. What is the number of points in space where electric Field intensity is zero due to this system?

Options

A. 0
B. 1
C. 2
D. None

Answer

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

### Step 1: Understand the System
We have two charges, \( Q_1 \) (positive) and \( Q_2 \) (negative), where \( |Q_1| > |Q_2| \). The charges are fixed at a distance \( r \) apart.

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

### Step 3: Identify Possible Locations for Zero Electric Field
1. **Between the Charges**: If we take a point between the two charges, the electric field due to \( Q_1 \) will point away from \( Q_1 \) (outward), and the electric field due to \( Q_2 \) will point towards \( Q_2 \) (inward). Since both fields are in the same direction, they cannot cancel each other out. Thus, there is no point between the charges where the electric field is zero.

2. **Outside the Charges**: We need to check the regions outside the line joining the two charges:
- To the left of \( Q_1 \): Here, the electric field due to \( Q_1 \) will point away from \( Q_1 \) (to the left) and the electric field due to \( Q_2 \) will point towards \( Q_2 \) (to the left as well). Since both fields point in the same direction, they cannot cancel each other out.
- To the right of \( Q_2 \): Here, the electric field due to \( Q_1 \) will point away from \( Q_1 \) (to the right) and the electric field due to \( Q_2 \) will point towards \( Q_2 \) (to the right). Again, both fields point in the same direction, so they cannot cancel each other out.

### Step 4: Conclusion
Since we have established that there is no point between the charges and no point outside the charges where the electric fields can cancel each other, we conclude that there is only **one point** in space where the electric field intensity is zero, and that point is located on the line joining the two charges, closer to the smaller charge \( Q_2 \).

### Final Answer
The number of points in space where the electric field intensity is zero due to this system is **1**.

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