When point charges q1 = +3.1 ìC and q2 = +5.1 ìC are brought near each other, each experiences a repulsive force of magnitude 0.54 N. Determine the distance between the charges.
kq2q1/d^2=.54
solve for d
To determine the distance between the charges, we can use Coulomb's Law, which states that the magnitude of the electrostatic force F between two point charges is given by:
F = k * |q1 * q2| / r^2
Where:
- F is the force between the charges,
- k is Coulomb's constant (9 × 10^9 N·m^2/C^2),
- q1 and q2 are the magnitudes of the charges, and
- r is the distance between the charges.
Given that F = 0.54 N, q1 = +3.1 μC (microCoulombs), q2 = +5.1 μC, and k = 9 × 10^9 N·m^2/C^2, we can rearrange the equation to solve for r:
r^2 = k * |q1 * q2| / F
Plugging in the given values:
r^2 = (9 × 10^9 N·m^2/C^2) * |(+3.1 μC) * (+5.1 μC)| / (0.54 N)
Now we can calculate it step by step:
First, convert the charges to Coulombs by dividing by 10^6:
r^2 = (9 × 10^9 N·m^2/C^2) * |(3.1 × 10^-6 C) * (5.1 × 10^-6 C)| / (0.54 N)
Next, evaluate the absolute value of the product of the charges:
r^2 = (9 × 10^9 N·m^2/C^2) * (3.1 × 10^-6 C) * (5.1 × 10^-6 C) / (0.54 N)
Multiply the charges:
r^2 = (9 × 10^9 N·m^2/C^2) * (3.1 × 10^-6 C * 5.1 × 10^-6 C) / (0.54 N)
Now, divide by the force:
r^2 = (9 × 10^9 N·m^2/C^2) * (3.1 × 10^-6 C * 5.1 × 10^-6 C) / (0.54 N)
Finally, take the square root of both sides to get the distance:
r = √[(9 × 10^9 N·m^2/C^2) * (3.1 × 10^-6 C * 5.1 × 10^-6 C) / (0.54 N)]
Calculating this expression should give you the distance between the charges.