Gauss' law problem with sphere

In summary, the conversation discusses the measurement of voltage in a spherical region that is spherically symmetrical. The radial electric field is found to be -Pwr^(p-1) and Gauss' Law is used to find the charge enclosed in a sphere of radius r. The charge enclosed by a sphere of radius r+dr is also found. The discussion then moves on to finding the differential charge and volume in the annular region between two concentric spheres of radii r and r+dr. Finally, finding the charge density, rho=rho(r)=?, is discussed. The relation between Gauss' Law and the given statement v(r)=wr^p is also mentioned.
  • #1
dpd069
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Homework Statement



In a spherical region, the voltage is measured to be spherically symmetrical, with v=v(r)=wr^p
a. Find the radial electric field.
b. Use Gauss’ Law to find the charge enclosed in a sphere of radius r.
c. Find the charge enclosed by a sphere of radius r+dr.
d. Find the differential charge enclosed in the annular region between two concentric spheres of radii r and r+dr.
e. Find the differential volume of the annular region between two concentric spheres of radii r and r+dr.
f. Find the charge density, rho=rho(r)=?


Homework Equations





The Attempt at a Solution


i am pretty sure that part a would be v(r)= - integral E(r) dr. so the radial electric field would be -Pwr^(p-1)

i am confused on how to do the rest. any help/hints would be appreciated.
 
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  • #2
Well what does gauss' law state?
 
  • #3
Gauss' law states that the flux of the electric field is equal to Q/epsilon0.

my question then is how do i relate that to the given statement v(r)=wr^p?
 

1. What is Gauss' law problem with a sphere?

Gauss' law is a fundamental law in electromagnetism that relates the distribution of electric charges to the resulting electric field. The problem with a sphere refers to using Gauss' law to calculate the electric field outside and inside of a charged sphere.

2. How do you solve a Gauss' law problem with a sphere?

To solve a Gauss' law problem with a sphere, you first need to draw a Gaussian surface around the sphere. This is a hypothetical surface that encloses the entire sphere and has a symmetry that makes the calculations easier. Then, you need to determine the charge enclosed within the Gaussian surface and use Gauss' law to calculate the electric field at any point on the surface.

3. What is the formula for Gauss' law with a sphere?

The formula for Gauss' law with a sphere is: E x 4πr² = Qenc/ε0, where E is the electric field, r is the radius of the Gaussian surface, Qenc is the charge enclosed within the surface, and ε0 is the permittivity of free space.

4. What is the difference between using Gauss' law with a sphere and a point charge?

The main difference between using Gauss' law with a sphere and a point charge is that a sphere has a finite size and a distribution of charge, while a point charge is a single, infinitesimally small point with a concentrated charge. This affects the calculation of the electric field and the shape of the electric field lines.

5. What are some real-world applications of Gauss' law with a sphere?

Gauss' law with a sphere has many real-world applications, such as in calculating the electric field of a charged conducting sphere, determining the electric potential of a charged sphere, and understanding the behavior of electric charges in a spherical capacitor. It is also used in the design and analysis of spherical antennas, which are used in satellite communication and radar systems.

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