Solving Gauss's Law Problem: Excess Electrons in Plastic Sphere

In summary, to produce an electric field of 1250N/C just outside the surface of a 23.0cm diameter plastic sphere, 45904610632 excess electrons must be distributed uniformly within the volume of the sphere. The equation used was E=Q/4*pi*ε*r^2, and after solving for the charge using the given equation and the radius, the number of electrons was found by dividing the charge by the charge of one electron. However, the mistake was made in using the diameter instead of the radius in the equation.
  • #1
A.J.710
53
1

Homework Statement



How many excess electrons must be distributed uniformly within the volume of an isolated plastic sphere 23.0cm in diameter to produce an electric field of 1250N/C just outside the surface of the sphere?

Homework Equations



E=Q/4*pi*ε*r^2


The Attempt at a Solution



I've attempted to find the charge using that equation and got 7.353*10^-9. Then to find the number of electrons I did 7.353*10^-9/1.602*10^-19 and I get 45904610632 electrons. It keeps saying I am wrong and I can't figure out why. Can anyone please tell me if I am doing something wrong.

Thanks
 
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  • #2
NEVERMIND. They threw in 23cm as the diameter and not the radius...
 

1. What is Gauss's Law and how is it used to solve problems?

Gauss's Law is a fundamental law in electromagnetism that relates the electric flux through a closed surface to the charge enclosed within that surface. It is used to solve problems involving the distribution of electric charge in a given space.

2. How do you approach solving a Gauss's Law problem involving excess electrons in a plastic sphere?

To solve a Gauss's Law problem involving excess electrons in a plastic sphere, you would begin by drawing a diagram of the problem and identifying the relevant variables, such as the radius of the sphere and the amount of excess charge. Then, you would apply the formula for Gauss's Law and use algebra to solve for the unknown variable.

3. What are the key concepts to understand when solving a Gauss's Law problem?

The key concepts to understand when solving a Gauss's Law problem are the concept of electric flux, which is the amount of electric field passing through a given area, and the concept of charge distribution, which refers to how electric charge is distributed within a given space. It is also important to understand the relationship between electric flux and charge enclosed, as described by Gauss's Law.

4. Can you provide an example of a Gauss's Law problem involving excess electrons in a plastic sphere?

Sure, an example of a Gauss's Law problem involving excess electrons in a plastic sphere could be: A plastic sphere with a radius of 10 cm contains an excess of 2.5 x 10^4 electrons. What is the electric flux through the surface of the sphere?

5. What are some common mistakes to avoid when solving a Gauss's Law problem?

One common mistake to avoid when solving a Gauss's Law problem is forgetting to take into account the direction of the electric field when calculating electric flux. It is also important to carefully consider the symmetry of the problem and choose an appropriate Gaussian surface to simplify the calculation. Additionally, it is important to use the correct units and pay attention to the sign of the charge enclosed in the equation.

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