Two electrons are suspended in a field and are 2.0 cm away from each other. How much would the electric force between two electron charges change if the distance between them is increased to 5.0cm?
Math.
Oh, let's give it a spin! So, you've got two electrons hanging out, 2.0 cm away from each other. But wait a second, one of them gets a sudden case of social distancing anxiety and moves 5.0 cm away instead. Now, we're tasked with finding out how the electric force between them would change.
Well, hang on to your electrons because I have an electrifying answer coming your way! The electric force between two charged objects (in this case, electrons) follows an inverse square law with distance. That means that if you increase the distance between them, the force will decrease. It's like when you move a little further away from someone during karaoke night because they're really bad at singing.
Specifically, the electric force changes in proportion to the square of the distance. So, if the distance between the electrons increases from 2.0 cm to 5.0 cm, the force will decrease by a factor of (2.0/5.0)^2. Crunching the numbers, you'll find that the force would be around 0.16 times its original value.
In summary, when those electrons decide to socially distance, the electric force between them decreases to about 16% of its original magnitude. It's like reducing the intensity of an awkward conversation by 84%.
To find out how the electric force changes when the distance between two charges is increased, we can use Coulomb's Law. Coulomb's Law states that the electric 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 electric force between the charges,
k is the electrostatic constant (k = 9.0 x 10^9 N m^2 / C^2),
q1 and q2 are the charges of the particles, and
r is the distance between the charges.
Given that the charges of both electrons are the same (since they are both electrons), let's assume q1 = q2 = e, where e is the elementary charge (e = 1.6 x 10^-19 C).
Initially, the distance between the electrons is 2.0 cm = 0.02 m. So, r = 0.02 m.
Using the formula, we can calculate the initial electric force (F_initial):
F_initial = (k * q1 * q2) / r^2
= (9.0 x 10^9 N m^2 / C^2) * (1.6 x 10^-19 C) * (1.6 x 10^-19 C) / (0.02 m)^2
Now, let's calculate the final electric force (F_final) when the distance between the electrons is increased to 5.0 cm = 0.05 m. So, r = 0.05 m.
F_final = (k * q1 * q2) / r^2
= (9.0 x 10^9 N m^2 / C^2) * (1.6 x 10^-19 C) * (1.6 x 10^-19 C) / (0.05 m)^2
To find out the change in electric force, we can calculate the ratio of F_final to F_initial:
Change in electric force = F_final / F_initial
Please note that due to the math involved, the actual values for the electric force and the change would be very small.
To calculate the change in electric force between two charges when the distance between them is changed, you can use Coulomb's Law. Coulomb's Law states that the magnitude of the electric 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. Mathematically, it can be expressed as:
F = k * ((q1 * q2) / r^2)
Where:
F is the electric force,
k is Coulomb's constant (k = 9 * 10^9 N m^2/C^2),
q1 and q2 are the charges of the two particles, and
r is the distance between them.
In this case, both electrons have the same charge, let's say it's q.
Initially, the distance between them is 2.0 cm, which is equivalent to 0.02 m. So, the initial force (F1) can be calculated as:
F1 = k * ((q * q) / (0.02)^2)
Now, if the distance between them is increased to 5.0 cm, which is equivalent to 0.05 m, we can calculate the new force (F2):
F2 = k * ((q * q) / (0.05)^2)
To find the change in force, we subtract the initial force from the new force:
Change in force = F2 - F1
You can substitute the values into the equations and evaluate them to obtain the final result.