Potentials of charge distribution

In summary, the question asks for the potential at the origin for a distribution of uniform charge lambda along a semicircle of radius R centered at the origin. To solve this, you need to consider the symmetry of the distribution and use the differential form of the potential function. By relating the charge density to the length, you can then solve the integral and find the potential at the origin.
  • #1
don23
10
0
The question says that charges are distributed with uniform charge lambda along a semicircle of radius R, centered at the origin of a coordinate system. What is the potential at the origin?

I am not sure how to approach this one. Can anyone help me set this up and solve it? Thanks!
 
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  • #2
Did you notice all dQ are at the same distance from O?
 
  • #3
For questions in electrostatics, the general strategy is to look for symmetry. Once you have established some sort of symmetry, use it to your advantage. You know the differential form of the potential function

[tex] V = \int \frac{k dq}{r}[/tex]
However from your geometric analysis, you only have r in your equation with no dr variable of integration. Instead you have a dq. You can relate the charge density to the length usually through something like

q=[tex]\rho[/tex]r where [tex]\rho[/tex] is the charge density, then
dq=[tex]\rho[/tex]dr

Substituting this in, you will finally be able to solve the integral and get your answer. Give it a try.
 
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1. What is charge distribution?

Charge distribution refers to the way in which electric charges are spread out or distributed in a given area or object. It describes the arrangement and amount of positive and negative charges within a system.

2. What are the types of charge distributions?

The two main types of charge distributions are continuous and discrete. Continuous charge distributions involve a continuous spread of charges, such as in a conducting wire. Discrete charge distributions, on the other hand, involve individual charges that are not spread out, such as in a group of particles.

3. How does charge distribution affect electric potential?

The distribution of charges affects the electric potential in a system. The electric potential is a measure of the electric potential energy per unit charge and is influenced by the location and magnitude of charges in a distribution. Areas with higher charge densities will have a higher electric potential, while areas with lower charge densities will have a lower electric potential.

4. What is a charge density?

Charge density refers to the amount of charge per unit volume or unit area in a given system. It is typically represented by the Greek letter rho (ρ) and is measured in coulombs per cubic meter or coulombs per square meter. Charge density is an important factor in determining the electric potential of a system.

5. How is charge distribution related to electric fields?

Charge distribution plays a significant role in creating and influencing electric fields. The electric field is a measure of the force exerted on a charge at a given point and is affected by the distribution of charges in a system. The greater the charge density, the stronger the electric field will be in that area.

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