Understanding Permittivity and Forces
When two charges, \( q_1 \) and \( q_2 \), are placed in different media characterized by varying permittivity, the electrostatic force between them is affected by the medium’s permittivity. The permittivity (\( \varepsilon \)) of a medium influences the electric field and the force experienced by the charges.
Permittivity Order
- Let the permittivities of the three media be:
- \( \varepsilon_a > \varepsilon_b > \varepsilon_c \)
Force Calculation
The electrostatic force \( F \) between two point charges in a medium can be expressed using Coulomb’s law:
\[ F = \frac{1}{4\pi \varepsilon} \cdot \frac{|q_1 q_2|}{r^2} \]
Where:
- \( F \) = electrostatic force
- \( \varepsilon \) = permittivity of the medium
- \( r \) = distance between the charges
Force in Different Media
- Given the same distance between the charges, the force in each medium can be expressed as:
- \( F_a = \frac{1}{4\pi \varepsilon_a} \cdot \frac{|q_1 q_2|}{r^2} \)
- \( F_b = \frac{1}{4\pi \varepsilon_b} \cdot \frac{|q_1 q_2|}{r^2} \)
- \( F_c = \frac{1}{4\pi \varepsilon_c} \cdot \frac{|q_1 q_2|}{r^2} \)
Force Order Determination
- Since \( \varepsilon_a > \varepsilon_b > \varepsilon_c \), we have:
- \( F_a < f_b="" />< f_c="" />
This means that the force experienced by the charges will be in the following order:
Final Force Order
- \( F_c > F_b > F_a \)
Conclusion
In summary, the electrostatic force between two charges decreases as the permittivity of the medium increases. Therefore, in a medium with the highest permittivity (medium \( a \)), the force is the weakest, while in the medium with the lowest permittivity (medium \( c \)), the force is the strongest.