Electric Potential Due to Unevenly Charged Disk - Help/Hints Needed

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In summary, the conversation is about finding the electric potential due to a disk of charge with an uneven charge distribution by integrating a complicated equation. The person is seeking advice on whether to use integration by parts or trigonometric substitution. Someone suggests using a substitution method and provides a hint on how to solve it. Another person mentions using a different substitution method involving u and dx. Finally, the original person thanks everyone for their advice.
  • #1
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i have to integrate to find the electric potential due to a disk of charge with an uneven charge distribution. i was able to set up the intergral but i can't solve it. should i do integration by parts (i tried it) or use something else. just give me a hint

int ( r^3/[(x^2 + r^2)]^.5) dr (x is a constant)

thanks
 
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  • #2
Make the substitution

[tex] r=x\sinh t [/tex]

Daniel.
 
  • #3
>.< I don't know Daniels way, Id go with trigonometric substitution, tan theta = r/x. Draw a triangle, you see that the hypotnuse is your denominator. Just solve for everything and sub them in, it reduces to [tex]x^3\int \tan^3 \theta \sec \theta d\theta[/tex].
 
  • #4
yea i figured it out. i did uv substitution, takeing u=r^2 and dx= r/(r^2+x^2) ^9.5)

thank you for everyone who gave advice. :D
 

1. What is the concept of electric potential?

The concept of electric potential refers to the amount of electric potential energy per unit charge at a point in an electric field. It is a measure of how much work is required to move a unit positive charge from infinity to that point in the electric field.

2. How is electric potential due to an unevenly charged disk calculated?

The electric potential due to an unevenly charged disk can be calculated using the equation V = kQ / R, where V is the electric potential, k is the Coulomb's constant, Q is the magnitude of the total charge on the disk, and R is the distance from the center of the disk to the point where the potential is being calculated.

3. What factors affect the electric potential of an unevenly charged disk?

The electric potential of an unevenly charged disk is affected by the magnitude and distribution of charge on the disk, as well as the distance from the center of the disk to the point where the potential is being calculated. The value of k, the Coulomb's constant, also affects the electric potential.

4. How does the electric potential of an unevenly charged disk change as you move away from the disk?

The electric potential of an unevenly charged disk decreases as you move away from the disk. This is because the electric potential is inversely proportional to the distance from the center of the disk, according to the equation V = kQ / R. As the distance increases, the denominator in the equation increases, resulting in a lower potential value.

5. What is the significance of calculating electric potential due to an unevenly charged disk?

Calculating electric potential due to an unevenly charged disk allows us to understand the behavior of electric fields and how they interact with charges. This is important in various fields, such as engineering and physics, as it helps in designing and understanding electronic devices, as well as predicting the behavior of charged particles in different scenarios.

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