Assertion (A): If two spherical conductors of different radii have the same surface charge densities, then their electric field intensities will be equal.
Reason (R ): Surface charge density `=("Total charge")/("area")`

Options

A. Both A and R are true and R is the correct explanation of A
B. Both A and Rare true but R is NOT the correct explanation of A
C. A is true but R is false
D. A is false and R is true

Explanation

To solve the problem, we need to analyze the assertion and the reason provided.

### Step-by-Step Solution:

1. **Understanding the Assertion (A)**:
- The assertion states that if two spherical conductors of different radii have the same surface charge densities, then their electric field intensities will be equal.

2. **Understanding Surface Charge Density**:
- Surface charge density (σ) is defined as the total charge (Q) per unit area (A) of the surface of the conductor.
- Mathematically, this is expressed as:
\[ \sigma = \frac{Q}{A} \]

3. **Calculating Electric Field Intensity for Spherical Conductors**:
- For a spherical conductor, the electric field (E) outside the sphere at a distance equal to the radius (r) is given by:
\[ E = \frac{kQ}{r^2} \]
where \(k\) is Coulomb's constant.

4. **Relating Charge and Surface Area**:
- The surface area (A) of a sphere is given by:
\[ A = 4\pi r^2 \]
- Therefore, the total charge (Q) can be expressed in terms of surface charge density (σ):
\[ Q = \sigma \cdot A = \sigma \cdot 4\pi r^2 \]

5. **Substituting Q into the Electric Field Formula**:
- For the first sphere with radius \(r\):
\[ E_1 = \frac{kQ_1}{r^2} = \frac{k(\sigma \cdot 4\pi r^2)}{r^2} = k \cdot 4\pi \sigma \]
- For the second sphere with radius \(R\):
\[ E_2 = \frac{kQ_2}{R^2} = \frac{k(\sigma \cdot 4\pi R^2)}{R^2} = k \cdot 4\pi \sigma \]

6. **Conclusion about Electric Fields**:
- From the calculations, we see that both electric fields \(E_1\) and \(E_2\) are equal:
\[ E_1 = E_2 = k \cdot 4\pi \sigma \]
- Thus, the assertion (A) is true.

7. **Understanding the Reason (R)**:
- The reason states that surface charge density is equal to total charge divided by area, which is a correct statement:
\[ \sigma = \frac{Q}{A} \]
- Therefore, the reason (R) is also true.

8. **Evaluating the Relationship Between A and R**:
- While both A and R are true, the reason does not directly explain why the electric fields are equal for the two spheres with different radii but the same surface charge density.

### Final Answer:
- Both assertion (A) and reason (R) are true, but R is not the correct explanation of A.