If two electrons (q = 1.60 x 10–19 C) are 1 m apart, what is the magnitude of the
electric force repelling the two electrons?
To calculate the magnitude of the electric force repelling the two electrons, you can use Coulomb's Law, which states that the force between two charged objects is directly proportional to the product of their 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 magnitude of the electric force
k is the electrostatic constant, approximately equal to 9 x 10^9 Nm^2/C^2
|q1 * q2| is the absolute value of the product of the charges
r is the distance between the charges
In this case, both electrons have the same charge (q = 1.60 x 10^-19 C), so the equation simplifies to:
F = k * (|q^2|) / r^2
Let's calculate the force:
F = (9 x 10^9 Nm^2/C^2) * ((1.60 x 10^-19 C)^2) / (1 m)^2
Simplifying the equation:
F = (9 x 10^9 Nm^2/C^2) * (2.56 x 10^-38 C^2) / (1 m^2)
F = (9 x 2.56) x (10^9 x 10^-38) Nm^2 / (C^2 x m^2)
F = 23.04 x 10^-29 Nm^2 / (C^2 x m^2)
Therefore, the magnitude of the electric force repelling the two electrons is 23.04 x 10^-29 N.