Calculate the force on an electron that is 3.8e-6 m from a proton.
To calculate the force on an electron that is a certain distance from a proton, we can use Coulomb's Law, which states that the force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
Coulomb's Law formula is given as:
F = k * (q1 * q2) / r^2
Where:
F is the force between the two charges,
k is the electrostatic constant (k = 9 * 10^9 N*m^2/C^2),
q1 and q2 are the charges of the particles, and
r is the distance separating the charges.
In this case, the charge of an electron is -1.6 * 10^(-19) C (Coulombs) and the charge of a proton is +1.6 * 10^(-19) C. The distance between them is 3.8 * 10^(-6) m.
Substituting the values into the formula:
F = (9 * 10^9 N*m^2/C^2) * ((-1.6 * 10^(-19) C) * (1.6 * 10^(-19) C)) / (3.8 * 10^(-6) m)^2
Simplifying the equation:
F = (9 * 10^9) * (2.56 * 10^(-38) C^2) / (1.44 * 10^(-11) m^2)
F = 1.6 * 10^(-28) N
Hence, the force on the electron that is 3.8 * 10^(-6) m from a proton is approximately 1.6 * 10^(-28) Newtons.