Two similar metal spheres, A and B, have charges of +2.0 x 10-6 coulomb and +1.0 x 10-6 coulomb, respectively. The magnitude of the electrostatic force on A due to B is 4.0N newtons. What is the magnitude of the electrostatic force on B due to A?
a)2 N
b)8 N
c)4 N
d)1 N
According to Newton's Third Law of Motion, the magnitude of the electrostatic force on B due to A will be equal to the magnitude of the electrostatic force on A due to B. Therefore, the magnitude of the electrostatic force on B due to A is also 4.0 N.
Therefore, the correct answer is c) 4 N.
To find the magnitude of the electrostatic force on B due to A, we can use Coulomb's Law, which states that the magnitude of the electrostatic force between two charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
Mathematically, Coulomb's Law can be expressed as:
F = k * (|q1| * |q2|) / r^2
Where:
F is the magnitude of the electrostatic force
k is the electrostatic constant (k ≈ 8.99 x 10^9 N m^2 / C^2)
|q1| and |q2| are the magnitudes of the charges
r is the distance between the charges
We are given:
|q1| = 2.0 x 10^-6 C (charge of A)
|q2| = 1.0 x 10^-6 C (charge of B)
F = 4.0 N (force on A due to B)
We can rearrange the equation to solve for the force on B due to A:
F = k * (|q1| * |q2|) / r^2
Rewriting the equation for the force on B due to A:
F = k * (|q2| * |q1|) / r^2 = 4.0 N
Now, we can substitute the given values into the equation:
4.0 N = k * (1.0 x 10^-6 C * 2.0 x 10^-6 C) / r^2
Simplifying the equation:
4.0 N = k * (2.0 x 10^-12 C^2) / r^2
To find the force on B due to A, we need to solve for the distance r. Rearranging the equation:
r^2 = k * (2.0 x 10^-12 C^2) / 4.0 N
Calculating the value:
r^2 = (8.99 x 10^9 N m^2 / C^2) * (2.0 x 10^-12 C^2) / 4.0 N
r^2 = 3.5976 x 10^-3 m^2
Taking the square root of both sides:
r ≈ 0.060 m
Now, with the value of r, we can calculate the force on B due to A using Coulomb's Law:
F = k * (|q1| * |q2|) / r^2
F = (8.99 x 10^9 N m^2 / C^2) * (2.0 x 10^-6 C * 1.0 x 10^-6 C) / (0.060 m)^2
Calculating the value:
F ≈ 5.32 N
Therefore, the magnitude of the electrostatic force on B due to A is approximately 5.32 N.
So, none of the given options (a) 2 N, b) 8 N, c) 4 N, d) 1 N) is correct.