Two electrostatic point charges of +60.0 uC and +50.c uC exert a repulsive force on each other of 175 N. What is the distance between the two charges?
d^2=(k*Q1*Q2)/F
d^2=(8.99*10^9)(60*10^-6uC)(50*10^-6uC)/175
d^2=0.154
square root of d^2= square root of 0.154
d=0.392m or 3.92cm
pineapple 3
Wrong. It's 1.2m since the equilibrium is involved in this problem.
To find the distance between the two charges, you can use Coulomb's law, which states that the magnitude of the electrostatic force between two point charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them.
Coulomb's Law formula: F = k * (|q1| * |q2|) / d^2
Where:
- F is the electrostatic force between the charges
- k is the electrostatic constant (k = 9 x 10^9 N m^2/C^2)
- |q1| and |q2| are the magnitudes of the charges
- d is the distance between the charges
Given:
- Charge 1 (q1): +60.0 μC
- Charge 2 (q2): +50.0 μC
- Electrostatic force (F): 175 N
Using this information, we can rearrange Coulomb's law to solve for the distance (d).
Step 1: Convert the charges to coulombs.
1 μC = 10^(-6) C
|q1| = 60.0 μC = 60.0 * 10^(-6) C = 6.0 * 10^(-5) C
|q2| = 50.0 μC = 50.0 * 10^(-6) C = 5.0 * 10^(-5) C
Step 2: Substitute the values into the formula.
175 N = (9 x 10^9 N m^2/C^2) * (6.0 * 10^(-5) C * 5.0 * 10^(-5) C) / d^2
Simplify the equation:
175 N * d^2 = (9 x 10^9 N m^2/C^2) * (6.0 * 10^(-5) C * 5.0 * 10^(-5) C)
Step 3: Calculate the right side of the equation.
(9 x 10^9 N m^2/C^2) * (6.0 * 10^(-5) C * 5.0 * 10^(-5) C) = 27 x 10^(-1) N m^2/C
Step 4: Divide both sides of the equation by 175 N.
d^2 = (27 x 10^(-1) N m^2/C) / 175 N
Step 5: Simplify the right side of the equation.
d^2 = 1.54 x 10^(-1) m^2/C
Step 6: Take the square root of both sides of the equation to solve for d.
d = √(1.54 x 10^(-1) m^2/C)
Step 7: Calculate the value of d.
d ≈ 0.392 m
Therefore, the distance between the two charges is approximately 0.392 meters.
Solve
F = k Q1 * Q2/R^2
You know everything but R. Look up the value of k