Assertion: The surface charge densities of two spherical conductors of different radii are equal. Then the electric field intensities near their surface are also equal.
Reason: Surface charge density is equal to charge per unit area.

Options

A. if both Assertion and Reason are true and the Reason is correct explanation of the Assertion.
B. If both Assertion and Reason are true but Reason is not the correct explanation of the Assertion.
C. if Assertion is true, but the Reason is false.
D. if both Assertion and Reason are false

Explanation

To solve the question, we need to analyze the given assertion and reason step by step.

### Step 1: Understanding the Assertion
The assertion states that the surface charge densities of two spherical conductors of different radii are equal, and as a result, the electric field intensities near their surfaces are also equal.

### Step 2: Define Surface Charge Density
Surface charge density (σ) is defined as the charge (Q) per unit area (A) on the surface of the conductor. For a spherical conductor, the surface area (A) is given by \( A = 4\pi r^2 \). Therefore, we can express the surface charge density as:
\[ \sigma = \frac{Q}{4\pi r^2} \]

### Step 3: Calculate Electric Field Near the Surface
The electric field (E) just outside the surface of a charged conductor is given by:
\[ E = \frac{kQ}{r^2} \]
where \( k \) is Coulomb's constant.

### Step 4: Substitute Charge in Terms of Surface Charge Density
For a spherical conductor, the total charge (Q) can be expressed in terms of the surface charge density (σ) and the surface area:
\[ Q = \sigma \cdot A = \sigma \cdot 4\pi r^2 \]
Substituting this into the expression for electric field:
\[ E = \frac{k(\sigma \cdot 4\pi r^2)}{r^2} = k \cdot 4\pi \sigma \]
This shows that the electric field near the surface depends only on the surface charge density and not on the radius of the sphere.

### Step 5: Conclusion about Electric Fields
Since both spherical conductors have the same surface charge density (σ), their electric fields (E1 and E2) near their surfaces will also be equal:
\[ E_1 = E_2 = k \cdot 4\pi \sigma \]

### Step 6: Analyze the Reason
The reason states that surface charge density is equal to charge per unit area. This is true, but it does not explain why the electric fields are equal when the surface charge densities are equal. The reason for the equality of electric fields is that the charge on the sphere scales with the square of the radius, which cancels out when calculating the electric field.

### Final Conclusion
- The assertion is true: If the surface charge densities are equal, the electric fields near their surfaces are also equal.
- The reason is true but does not adequately explain the assertion.

### Answer:
The correct option is that both statements are true, but the reason does not explain the assertion.

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