Two point charges of different magnitudes and of opposite signs are separated by some distance. There can be.

Options

A. only on the point in space where net electric field intensity is zero.
B. only two points in space where net electric potential is zero
C. infinite number of points in space where net electric field intensity is `0`
D. infinite number of points in space where net electric potential is zero.

Explanation

To solve the problem regarding the two point charges of different magnitudes and opposite signs, we need to analyze the conditions under which the electric field intensity and electric potential can be zero.

### Step 1: Understanding the Setup
We have two point charges, \( Q_1 \) (positive) and \( Q_2 \) (negative), with \( |Q_1| > |Q_2| \). Let's assume:
- \( Q_1 = +5 \, \mu C \)
- \( Q_2 = -2 \, \mu C \)

These charges are separated by some distance, say \( d \).

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

#### Finding Points Where Electric Field is Zero
1. **Between the Charges**:
- The electric field from \( Q_1 \) points away from it, while the field from \( Q_2 \) points towards it. Since \( Q_1 \) is larger, the electric field cannot be zero between the two charges.

2. **Outside the Charges**:
- To the left of \( Q_2 \) (negative charge), the electric field due to \( Q_2 \) is directed towards it (to the left), and the electric field due to \( Q_1 \) is directed away from it (to the right). There can be a point where these fields are equal in magnitude but opposite in direction.
- To the right of \( Q_1 \) (positive charge), the electric field due to \( Q_1 \) is directed away from it, and the electric field due to \( Q_2 \) is directed towards it. However, since \( Q_1 \) is larger, the electric field will not be zero here.

Thus, there is **only one point in space** (to the left of \( Q_2 \)) where the net electric field intensity is zero.

### Step 3: Electric Potential
The electric potential \( V \) due to a point charge is given by:
\[ V = \frac{k Q}{r} \]
where \( r \) is the distance from the charge.

#### Finding Points Where Electric Potential is Zero
1. **Potential Calculation**:
- The potential due to \( Q_1 \) is positive and increases as we move closer to it.
- The potential due to \( Q_2 \) is negative and increases (becomes less negative) as we move closer to it.

2. **Finding Zero Potential**:
- There can be multiple points in space where the positive potential from \( Q_1 \) can equal the negative potential from \( Q_2 \).
- For example, if we take a point very far away from both charges, the potentials from both charges will approach zero, but they can also cancel each other out at various distances.

Thus, there are **infinite points in space** where the net electric potential is zero.

### Conclusion
From our analysis:
- There is **only one point** in space where the net electric field intensity is zero.
- There are **infinite points** in space where the net electric potential is zero.