A charge of 2.1 nC and a charge of 4.7 nC are separated by 57.90 cm. Find the equilibrium position for a -4.7 nC charge.
____ cm from the 2.1 nC charge.
what is the answer? and how did you get it? thaanks
The equilibrium position is between the two charges,there tha attractive forces to the +2.1nC and +4.7 nC charges are equal and opposite. If x is the distance from the 2.1 nC charge, require that
2.1/x^2 = 4.7/(57.9-x)^2
Solve that equation for x, which will be in centimeters. The -4.7 nC charge cancels out, as does the Coulomb constant, making the solution easy. You can use nC for charge and cm for distance on both sides of the equation.
(57.9-x)/x = sqrt(4.7/2.1) = 1.496
57.9/x = 2.496
x = ?
To find the equilibrium position for a -4.7 nC charge from a 2.1 nC charge, we can use Coulomb's Law. Coulomb's Law states that the force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
The formula for Coulomb's Law is:
F = k * (|q1| * |q2|) / r^2
Where:
- F is the electrostatic force between the charges
- k is the electrostatic constant, approximately 9 × 10^9 N m^2/C^2
- |q1| and |q2| are the magnitudes of the charges
- r is the distance between the charges
In this case, we have a charge of 2.1 nC and a charge of 4.7 nC separated by 57.90 cm. We want to find the equilibrium position for a -4.7 nC charge, so we can set up the equation as follows:
F1 = F2
k * (|q1| * |q3|) / r1^2 = k * (|q2| * |q3|) / r2^2
Where:
- F1 and F2 are the forces exerted by q1 and q2 on q3, respectively
- |q3| is the magnitude of the -4.7 nC charge we want to find the equilibrium position for
- r1 is the distance between q1 and q3 (unknown)
- r2 is the distance between q2 and q3 (desired equilibrium position)
Simplifying the equation, we have:
(|q1| * |q3|) / r1^2 = (|q2| * |q3|) / r2^2
Since |q1| = 2.1 nC, |q2| = 4.7 nC, and |q3| = -4.7 nC, we can substitute these values into the equation:
(2.1 * -4.7) / r1^2 = (4.7 * -4.7) / r2^2
Simplifying further:
-9.87 / r1^2 = -22.09 / r2^2
Cross multiplying:
r2^2 / r1^2 = 22.09 / 9.87
Taking the square root of both sides:
r2 / r1 = sqrt(22.09 / 9.87)
Simplifying:
r2 = r1 * sqrt(22.09 / 9.87)
Substituting the given distance of 57.90 cm for r1:
r2 = 57.90 cm * sqrt(22.09 / 9.87)
Evaluating this calculation, we find that the equilibrium position for a -4.7 nC charge from the 2.1 nC charge is approximately 82.73 cm. Therefore, the answer is 82.73 cm from the 2.1 nC charge.