Two charges placed in air repel each other by a force of `10^(-4)N`. When oil is introduced between the charges, then the force becomes `2.5 xx 10^(-5)N`
The dielectric constant of oil is

Options

A. 2.5
B. 0.25
C. 2
D. 4

Answer

To find the dielectric constant of oil, we can follow these steps:

### Step 1: Understand the relationship between force, charges, and dielectric constant
The electrostatic force \( F \) between two charges \( q_1 \) and \( q_2 \) in a medium with dielectric constant \( k \) is given by the formula:

\[ F = \frac{1}{4\pi \epsilon_0} \cdot \frac{q_1 q_2}{r^2} \cdot \frac{1}{k} \]

Where:
- \( \epsilon_0 \) is the permittivity of free space.
- \( r \) is the distance between the charges.

### Step 2: Write the force in air
In air, the dielectric constant \( k \) is approximately 1. The force \( F \) in air is given as:

\[ F = 10^{-4} \, \text{N} \]

Thus, we can express it as:

\[ 10^{-4} = \frac{1}{4\pi \epsilon_0} \cdot \frac{q_1 q_2}{r^2} \cdot \frac{1}{1} \]

### Step 3: Write the force in oil
When oil is introduced, the force \( F' \) becomes:

\[ F' = 2.5 \times 10^{-5} \, \text{N} \]

In this case, the force can be expressed as:

\[ 2.5 \times 10^{-5} = \frac{1}{4\pi \epsilon_0} \cdot \frac{q_1 q_2}{r^2} \cdot \frac{1}{k} \]

### Step 4: Relate the two forces
From the two equations, we can relate the forces:

\[ F' = \frac{F}{k} \]

Substituting the known values:

\[ 2.5 \times 10^{-5} = \frac{10^{-4}}{k} \]

### Step 5: Solve for \( k \)
Rearranging the equation to solve for \( k \):

\[ k = \frac{10^{-4}}{2.5 \times 10^{-5}} \]

Calculating \( k \):

\[ k = \frac{10^{-4}}{2.5 \times 10^{-5}} = \frac{10}{2.5} = 4 \]

### Conclusion
The dielectric constant of oil is \( k = 4 \).

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