Question

Rearrange the Coulomb's Law formula to find distance(r)

Answer 1

Coulomb's law describes the magnitude of the electrostatic force between two electric charges. The Coulomb's law formula is:
  F = Ke * q1 * q2 / r2

Where:
  q1: Charge of object 1
  q2: Charge of object 2
  r: Distance between the two objects
  F: Force between the two objects. A positive force implies a repulsive interaction, while a negative force implies an attractive interaction
  Ke = Coulomb Constant, 8.9875517873681764 * 109 N.m2.C-2

Coulomb's Law Examples:
What is the magnitude of the force between two protons which are 1.6E10-6 meters apart?

The charge of 1 proton is +1e (+1.602E-19 C).

F = 8.9875517873681764 * 109 * 1.602E-19 * 1.602E-19 / (1.6E-6 * 1.6 E-6) = 9 * 10-17 N


Source- http://www.endmemo.com/physics/coulomb.php




f = k (q^1)(q^2)/r^2

both sides by r^2 Multiply
fr^2/r^2 = kq^3/r^2

both sides by r^2 divide 
f = kq^3/r^2


Answer:
f = kq^3/r^2



Hope this helps!!!!

Answer 2

Answer:

distance in terms of force is given as

$r = \sqrt{\frac{kq_1q_2}{f}}$

Explanation:

here as we know that the force between two charges placed at distance "r" is given by Coulomb's law

It is given by the formula

$F = \frac{kq_1q_2}{r^2}$

now we have to rearrange it for finding the distance

so here we will multiply both sides by square of the distance

$f \times r^2 = kq_1q_2$

now we will divide both sides force "f"

$r^2 = \frac{kq_1q_2}{f}$

now square root both sides

$r = \sqrt{\frac{kq_1q_2}{f}}$