Gauss's Law, electric field of sphere

In summary, a nonconducting sphere with a radius of 10.00 cm has a uniform volume charge density of 410 nC/m3. The total charge of the sphere is 1.717 nC. At r = 2.10 cm, the electric field is ____ N/C. At r = 9.90 cm, the electric field is ____ kN/C. At r = 10.10 cm, the electric field is ____ N/C. And at r = 13.6 cm, the electric field is ____ N/C. The equation used to calculate these values was E = Qr/[(4*pi*R^3)*8.85x10^(-12)].
  • #1
krtica
50
0
Q:
A nonconducting sphere of radius 10.00 cm carries a uniform volume charge density ρ = 410 nC/m3.

(a) What is the total charge of the sphere?
1.717 nC

Find the electric field at the following radii.

(b) r = 2.10 cm
_____N/C

(c) r = 9.90 cm
_____kN/C

(d) r = 10.10 cm
_____N/C

(e) r = 13.6 cm
_____N/C


My attempt at the problem, after manipulating the equation EV=charge inside/[8.85x10^(-12)], was just to insert values into E=Qr/[(4*pi*R^3)*8.85x10^(-12)]; where Q is defined as the total charge, r the radius asked to calculate and R the initial radius.
 
Physics news on Phys.org
  • #2
Your attempt is correct.
 
  • #3
Thank you for responding.
 

1. What is Gauss's Law?

Gauss's Law is a fundamental law in electromagnetism that relates the electric flux through a closed surface to the enclosed electric charge. It is named after the German mathematician and physicist Carl Friedrich Gauss.

2. How is Gauss's Law applied to find the electric field of a sphere?

To find the electric field of a sphere, we use Gauss's Law by choosing a Gaussian surface in the shape of a sphere that encloses the charge. Then, we use the formula E = Q/4πε0r2, where E is the electric field, Q is the enclosed charge, ε0 is the permittivity of free space, and r is the radius of the sphere.

3. What is the significance of the electric field of a sphere?

The electric field of a sphere is significant because it helps us understand how the electric field behaves around a charged spherical object. It also allows us to calculate the force experienced by a charged particle placed in the electric field of a sphere.

4. Does the electric field of a sphere depend on the location of the charge within the sphere?

No, according to Gauss's Law, the electric field of a sphere only depends on the total enclosed charge and the distance from the center of the sphere. It does not depend on the distribution or location of the charge within the sphere.

5. Can Gauss's Law be applied to non-spherical objects?

Yes, Gauss's Law can be applied to any closed surface, regardless of its shape. However, for more complex objects, the calculation of the electric field may be more challenging and may require the use of calculus.

Similar threads

  • Introductory Physics Homework Help
Replies
17
Views
404
Replies
1
Views
152
  • Introductory Physics Homework Help
Replies
5
Views
227
  • Introductory Physics Homework Help
Replies
26
Views
588
  • Introductory Physics Homework Help
Replies
10
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
901
  • Introductory Physics Homework Help
Replies
12
Views
1K
  • Introductory Physics Homework Help
Replies
6
Views
833
  • Introductory Physics Homework Help
Replies
18
Views
3K
  • Introductory Physics Homework Help
Replies
3
Views
1K
Back
Top