Integrating an inverse square to find U

In summary, the conversation is about someone asking for an explanation on the derivation of Electric Potential Energy and the confusion around the integration of the work equation. They eventually realize it is a calculus issue and discuss the power rule and the steps to find the definite integral, which leads to the final equation of kQq (1/r_a - 1/r_b).
  • #1
Imabioperson
5
0
Hello everyone,

This is probably going to come off as a very silly question. However, I have not had calculus in several years. I was angry that my physics textbook did not have a derivation of Electric Potential Energy. So, I finally came across it, and I see that the integration of the work equation from some point, r_a to another point, r_b yields, kQq (1/r_a - 1/r_b). Can someone explain to me where, (1/r_a - 1/r_b) is coming from?
 
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  • #2
Sounds like you realize it's a calculus issue. Review the power rule.
 
  • #3
So, if you take the anti-derivative FIRST... we yield r^-1 in the numerator. And then, we will take the definite integral, leaving us with (1/upper limit - 1/lower limit)? And then do I switch the sign because of the relation between Work and Potential energy?
 
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FAQ: Integrating an inverse square to find U

What is the purpose of integrating an inverse square to find U?

Integrating an inverse square is a mathematical process used to find the potential energy, denoted as U, of a system. It allows scientists to understand the forces at work within a system and how they affect the energy of the system.

How does one integrate an inverse square to find U?

To integrate an inverse square, one must use the formula U = -Gm1m2/r, where G is the gravitational constant, m1 and m2 are the masses of the objects in the system, and r is the distance between them. This formula is then integrated with respect to r to find the potential energy, U.

Why is the inverse square law important in this process?

The inverse square law states that the force between two objects is inversely proportional to the square of the distance between them. This law is important in integrating an inverse square to find U because it helps determine the relationship between the force and the potential energy of a system.

Can integrating an inverse square also be used to find the kinetic energy of a system?

No, integrating an inverse square is specifically used to find the potential energy of a system. To find the kinetic energy, one must use the formula KE = 1/2mv^2, where m is the mass of the object and v is its velocity.

What are some real-life applications of integrating an inverse square to find U?

Integrating an inverse square to find U has many real-life applications, including determining the orbits of planets and satellites, calculating the potential energy of chemical bonds, and understanding the behavior of electrical charges in an electric field.

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