Which of the following statements are correct?
a. The electrostatic force does not depend on medium in which the charges are placed.
b. The electrostatic force between two charges does not exist in vacuum
c. The gravitational force between masses can be usually neglected in comparison with electrostatic force
d. Any excess charge given to a conductor, not always resides on the outer surface of the conductor.

Options

A. both a and c
B. only c
C. both c and d
D. all

Answer

To determine which of the statements are correct, we will analyze each statement one by one.

### Step 1: Analyze Statement A
**Statement A:** The electrostatic force does not depend on the medium in which the charges are placed.

**Analysis:** The electrostatic force (Coulomb's force) is given by the formula:

\[ F = k \frac{|q_1 q_2|}{r^2} \]

where \(k\) is the Coulomb's constant, which can also be expressed as:

\[ k = \frac{1}{4 \pi \epsilon_0 \epsilon_r} \]

Here, \(\epsilon_r\) is the relative permittivity of the medium. Since \(\epsilon_r\) depends on the medium, the electrostatic force does indeed depend on the medium.

**Conclusion:** Statement A is **incorrect**.

### Step 2: Analyze Statement B
**Statement B:** The electrostatic force between two charges does not exist in vacuum.

**Analysis:** The electrostatic force can exist in a vacuum. In vacuum, the value of \(\epsilon_r\) is 1, and the force still acts between charges according to Coulomb's law. Therefore, electrostatic forces can exist in a vacuum.

**Conclusion:** Statement B is **incorrect**.

### Step 3: Analyze Statement C
**Statement C:** The gravitational force between masses can usually be neglected in comparison with the electrostatic force.

**Analysis:** The electrostatic force is significantly stronger than the gravitational force. In fact, the electrostatic force can be about \(10^7\) times stronger than the gravitational force for the same amount of charge and mass. Therefore, in many scenarios, the gravitational force can indeed be neglected when compared to the electrostatic force.

**Conclusion:** Statement C is **correct**.

### Step 4: Analyze Statement D
**Statement D:** Any excess charge given to a conductor does not always reside on the outer surface of the conductor.

**Analysis:** According to electrostatic principles, any excess charge placed on a conductor will redistribute itself and reside on the outer surface of the conductor. This is a fundamental property of conductors in electrostatics.

**Conclusion:** Statement D is **incorrect**.

### Final Conclusion
The only correct statement among the four is **Statement C**.

### Summary of Correctness:
- Statement A: Incorrect
- Statement B: Incorrect
- Statement C: Correct
- Statement D: Incorrect