Question

Two electrons in a vacuum exert force of F = 3.8E-09 N on each other. They are then moved such that they are separated by x = 8.2 times their original distance. What is the force that the electrons experience at the new distance, F_n, in newtons? Numeric: A numeric value is expected and not an expression. F_n = ______________________________ How far apart were the electrons originally in meters? Numeric: A numeric value is expected and not an expression. d = _________________________________

Answer 1

The new force (F_n) experienced by the electrons when they are moved to 8.2 times their original distance is 5.664E-11 N. The original distance between the electrons cannot be determined from the information provided since the charge of an electron and Coulomb's constant are needed for the calculation.

Step-by-step explanation:

The force between two charges, such as electrons, is determined by Coulomb's law which states that the force (F) between two charges is proportional to the product of the charges and inversely proportional to the square of the distance (r) between them. The formula is given as F = k * q1 * q2 / r^2, where k is Coulomb's constant.

Since the electrons are moved to a distance of 8.2 times their original distance, the new force (F_n) can be found by dividing the original force by 8.2 squared. F_n = F / (8.2)^2. Using the given original force F = 3.8E-09 N, the new force is calculated as F_n = 3.8E-09 N / (8.2)^2 resulting in F_n = 5.664E-11 N.

To find the original distance between the electrons, we would use Coulomb's law rearranged to solve for r. However, since the charge of an electron and Coulomb's constant are not provided in the question, we cannot compute the exact original distance.

Answer 2

F_n = 5.65E-11 N

d = 1.20682E-31 m

Step-by-step explanation:

F = 3.8E-09 N

where

m = Mass of electron = 9.109E−31 kilograms

G = Gravitational constant = 6.67E-11 m³/kgs²

x = Distance between them

`F=G(m^2)/(x^2)\\\Rightarrow 3.8E-09=G(m^2)/(x^2)`

For
`F_n`

`F_n=G(m^2)/(x^2)\\\Rightarrow F_n=G(m^2)/((8.2x)^2)\\\Rightarrow F_n=G(m^2)/(67.24x^2)`

Dividing the above equations we get

`(F)/(F_n)=(G(m^2)/(x^2))/(G(m^2)/(67.24x^2))\\\Rightarrow (F)/(F_n)=67.24\\\Rightarrow F_n=(F)/(67.24)\\\Rightarrow F_n=(3.8E-09)/(67.24)\\\Rightarrow F_n=5.65E-11\ N`

F_n = 5.65E-11 N

`F=G(m^2)/(x^2)\\\Rightarrow x=\sqrt{(Gm^2)/(F)}\\\Rightarrow x=\sqrt{(G)/(F)}m\\\Rightarrow x=\sqrt{(6.67E-11)/(3.8E-09)}9.109E-31\\\Rightarrow x=1.20682E-31\ m`

d = 1.20682E-31 m