Two charges placed at a distance r apart exert force F on each other at what distance will these charges experience same force in medium of dielectric constant K.
F=c/kr^2
so F is proportional to 1/K
To find the distance at which two charges will experience the same force in a medium with dielectric constant K, we can use Coulomb's law and the concept of electric field in a dielectric medium.
Coulomb's law states that the force (F) between two charges (q1 and q2) separated by a distance (r) in a vacuum is given by:
F = (1/(4πε₀)) * (q1 * q2) / r^2
Where ε₀ is the vacuum electric constant.
In a dielectric medium with dielectric constant K, the force between the charges is modified as:
F' = (1/(4πε₀K)) * (q1 * q2) / r^2
To find the distance at which these charges will experience the same force (F = F'), we can equate the two expressions:
(1/(4πε₀)) * (q1 * q2) / r^2 = (1/(4πε₀K)) * (q1 * q2) / r^2
Simplifying the equation:
1/K = 1
K = 1
Therefore, the dielectric constant K does not affect the distance at which the charges will experience the same force. The distance at which the charges experience the same force remains the same as in a vacuum, which is the original distance r.
To find the distance at which the charges will experience the same force in a medium of dielectric constant K, we can use Coulomb's Law. Coulomb's Law states that the force (F) between two charges (q1 and q2) is given by the equation:
F = (1 / (4πε)) * (q1 * q2 / r^2)
where ε is the electric constant (ε ≈ 8.854 x 10^-12 C^2 / N*m^2).
In the presence of a dielectric medium, the electric constant gets multiplied by the dielectric constant (K) of the medium. So, the modified equation becomes:
F' = (1 / (4πεK)) * (q1 * q2 / r^2)
Since we want to find the distance at which the charges experience the same force, we can set F' equal to F:
(1 / (4πεK)) * (q1 * q2 / r^2) = (1 / (4πε)) * (q1 * q2 / r'^2)
Here, r' is the distance at which the charges experience the same force.
We can cancel out the common terms and rearrange the equation to solve for r':
(1 / K) * (1 / r^2) = 1 / r'^2
(r')^2 = (r^2) * K
Taking the square root of both sides, we can find the distance at which the charges experience the same force:
r' = √(r^2 * K)
Therefore, the distance at which the charges will experience the same force in a medium of dielectric constant K is given by the square root of the product of the original distance (r) squared and the dielectric constant (K).