Two electrostatic point charges of +54.0 ¦ÌC
and +47.0 ¦ÌC exert a repulsive force on each
other of 189 N.
What is the distance between the two
charges? The value of the Coulomb constant
is 8.98755 ¡Á 109 N ¡¤ m2/C2.
Answer in units of m
Use the equation F=k|q1||q2|/r^2 and plug in your givens
To find the distance between the two charges, we can use Coulomb's law equation:
F = (k * |q1 * q2|) / r^2
where F is the force, k is the Coulomb constant, q1 and q2 are the charges, and r is the distance between the charges.
Given that the force (F) is 189 N, the Coulomb constant (k) is 8.98755 × 10^9 N · m^2/C^2, charge 1 (q1) is +54.0 μC, and charge 2 (q2) is +47.0 μC, we can rearrange the equation to solve for the distance (r):
r^2 = (k * |q1 * q2|) / F
Plugging in the values:
r^2 = (8.98755 × 10^9 N · m^2/C^2 * |54.0 × 10^-6 C * 47.0 × 10^-6 C|) / 189 N
r^2 = (8.98755 × 10^9 N · m^2/C^2 * 2.538 × 10^-9 C^2) / 189 N
r^2 = (2.28289 × 10^-3 N · m^2) / 189 N
r^2 ≈ 1.211 × 10^-5 m^2
To get the distance (r), we take the square root of both sides:
r ≈ √(1.211 × 10^-5 m^2)
r ≈ 0.00348 m
Therefore, the distance between the two charges is approximately 0.00348 m.