If two charges are kept in a material of dielectric constant what is the ratio of force between them:

Options

A. `16:1`
B. `2:1`
C. `4:1`
D. `1:1`

Explanation

To find the ratio of the force between two charges placed in a dielectric material, we can follow these steps:

### Step 1: Understand the Force Between Charges
The force \( F \) between two point charges \( q_1 \) and \( q_2 \) in a vacuum is given by Coulomb's law:
\[ F = \frac{k \cdot |q_1 \cdot q_2|}{r^2} \]
where \( k \) is Coulomb's constant, and \( r \) is the distance between the charges.

### Step 2: Introduce the Dielectric Constant
When the charges are placed in a dielectric medium, the force between them is reduced by a factor equal to the dielectric constant \( \kappa \) of the material. The force \( F' \) in a dielectric medium is given by:
\[ F' = \frac{F}{\kappa} = \frac{k \cdot |q_1 \cdot q_2|}{\kappa \cdot r^2} \]

### Step 3: Calculate the Ratio of Forces
To find the ratio of the force in the dielectric medium \( F' \) to the force in a vacuum \( F \), we can express it as:
\[ \text{Ratio} = \frac{F'}{F} = \frac{\frac{k \cdot |q_1 \cdot q_2|}{\kappa \cdot r^2}}{\frac{k \cdot |q_1 \cdot q_2|}{r^2}} = \frac{1}{\kappa} \]

### Conclusion
Thus, the ratio of the force between the two charges when placed in a dielectric material to the force between them in a vacuum is:
\[ \text{Ratio} = \frac{1}{\kappa} \]