Show that this equation is inverse square

In summary, the equation F = k(Q2*Q1)/(r^2) represents an inverse square law, where the force (F) between two charges (Q1 and Q2) is inversely proportional to the square of the distance (r) between them. The constant k remains the same for all values of Q1 and Q2, while only r changes. This means that as r increases, the force between the charges decreases exponentially.
  • #1
brycenrg
95
2

Homework Statement


F = k(Q2*Q1)/(r^2)

Homework Equations

The Attempt at a Solution


I asked my teacher and he said that this is an inverse square law. Didn't say anything else. He also mentioned k is constant.

I assume i can plug in random values and see if there is a pattern... k=1 for all
Set 1, q1 = 2, q2 = 4, r = 5
F1 = 8/25
Set 2, q1 = 1 q2 = 5, r = 4
F2 = 5/16
I plugged in random values but i don't really get it.
What is inverse of what? I see that the r is squared and its below the kq1q2. I'm stuck.

Any advice is appreciated.
 
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  • #2
This function is dependent on the inverse squared of r, which is usually the distance between the locations of Q1 and Q2.
 
  • #3
brycenrg said:

Homework Statement


F = k(Q2*Q1)/(r^2)

Homework Equations

The Attempt at a Solution


I asked my teacher and he said that this is an inverse square law. Didn't say anything else. He also mentioned k is constant.

I assume i can plug in random values and see if there is a pattern... k=1 for all
Set 1, q1 = 2, q2 = 4, r = 5
F1 = 8/25
Set 2, q1 = 1 q2 = 5, r = 4
F2 = 5/16
I plugged in random values but i don't really get it.
What is inverse of what? I see that the r is squared and its below the kq1q2. I'm stuck.

Any advice is appreciated.
What RUber said . ...

So, pick values for Q1 and Q2 and stay with those. Then plug-in various values for r.
 
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  • #4
SammyS said:
What RUber said . ...

So, pick values for Q1 and Q2 and stay with those. Then plug-in various values for r.
Thank you so, r is the only value that is changing?
 
  • #6
Ray Vickson said:
Yes. That is exactly what "inverse square" means. Google is your friend; see
https://en.wikipedia.org/wiki/Inverse-square_law
Thank you, Yeah i googled it but thought the Q's changed as well. So it didn't make sense. Sometimes i need someone to explain it to me like I am 5.
 
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Likes RUber

FAQ: Show that this equation is inverse square

What does it mean for an equation to be inverse square?

For an equation to be inverse square, it means that the dependent variable is inversely proportional to the square of the independent variable. This relationship is represented by the equation y = k/x^2, where k is a constant and x is the independent variable.

How can you show that an equation is inverse square?

To show that an equation is inverse square, you must plot the data points and observe the relationship between the dependent and independent variables. If the data follows a pattern where the dependent variable decreases as the square of the independent variable increases, then the equation is inverse square.

What are some common examples of inverse square equations?

Inverse square equations can be found in various fields of science, such as Newton's law of universal gravitation (F = Gm1m2/r^2), Coulomb's law of electrostatic force (F = kq1q2/r^2), and the law of intensity of light (I = k/d^2). These equations all follow the inverse square relationship.

Are there any exceptions to the inverse square relationship?

Yes, there are some cases where the inverse square relationship does not apply. For example, the force between two magnetic poles follows an inverse cube relationship (F = kq1q2/r^3). Additionally, some real-life situations may have factors that affect the relationship and deviate from the inverse square law.

How is the inverse square relationship important in science?

The inverse square relationship is crucial in many areas of science, such as physics, astronomy, and engineering. It allows us to understand the relationship between variables and make predictions about how they will change. This relationship also helps us to calculate important values, such as force, intensity, and energy.

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