The magnitude of electric force, F is

Options

A. directly proportional to the multiplication of both charges.
B. directly proportional to the distance between both charges.
C. directly proportional to the square of the distance between both charges.
D. constant.

Explanation

To solve the question regarding the magnitude of electric force \( F \) between two charges, we can refer to Coulomb's Law. Here’s a step-by-step solution:

### Step 1: Understand Coulomb's Law
Coulomb's Law states that the electric force \( F \) between two point charges \( q_1 \) and \( q_2 \) is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance \( r \) between them.

### Step 2: Write the Mathematical Expression
The mathematical expression for Coulomb's Law can be written as:
\[ F = k \frac{|q_1 \cdot q_2|}{r^2} \]
where \( k \) is Coulomb's constant.

### Step 3: Analyze the Proportional Relationships
From the expression:
- The force \( F \) is **directly proportional** to the product of the charges \( q_1 \) and \( q_2 \).
- The force \( F \) is **inversely proportional** to the square of the distance \( r \) between the charges.

### Step 4: Evaluate the Options
Now, let's evaluate the options given in the question:
1. **Directly proportional to the multiplication of both charges**: This is correct.
2. **Directly proportional to the distance between both charges**: This is incorrect; it is inversely proportional.
3. **Directly proportional to the square of the distance between both charges**: This is also incorrect; it is inversely proportional to the square of the distance.
4. **Constant**: This is incorrect as well; the force depends on the charges and the distance.

### Conclusion
The correct option is the first one: **Directly proportional to the multiplication of both charges**.

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