MAgnitude of electric Field

In summary, the magnitude of the electric field at 10.0 cm, 40.0 cm, and 60.0 cm from the center of a solid sphere with a radius of 40.0 cm and a total positive charge of 46.0 µC is 6.892333333e15, calculated using the equation E=kq/r^2 and Gauss's Law. The ratio of the charge enclosed by the sphere to the charge of the entire sphere is Q'=Q(r^3/R^3).
  • #1
musicman05
4
0

Homework Statement


A solid sphere of radius 40.0 cm has a total positive charge of 46.0 µC uniformly distributed throughout its volume. Calculate the magnitude of the electric field:

10.0 cm from the center of the sphere
40.0 cm from the center of the sphere
60.0 cm from the center of the sphere



Homework Equations



E=kq/r^2



The Attempt at a Solution



8.99e9*46e6/60cm=6.892333333e15
 
Physics news on Phys.org
  • #2
Let's call the charge enclosed by a sphere of radius r (with r < R) Q', and the charge of the entire sphere, Q.

The ratio of the charges is thus [tex]\frac{Q'}{Q}=\frac{\frac{4}{3}\pi r^3}{\frac{4}{3}\pi R^3}[/tex]

or:

[tex]Q'=Q\frac{r^3}{R^3}[/tex]

Using this, and the fact that [tex]\int \vec{E}.\vec{da}=\frac{q}{\epsilon _0}[/tex] from Gauss's Law.

You can calculate the electric field at any point within the sphere.
 
Last edited:

1. What is the definition of the magnitude of electric field?

The magnitude of electric field is a measure of the strength of an electric field at a specific point in space. It is defined as the force per unit charge experienced by a positive test charge placed at that point.

2. How is the magnitude of electric field calculated?

The magnitude of electric field can be calculated using the equation E = F/q, where E is the electric field, F is the electric force, and q is the test charge.

3. What is the unit of measurement for the magnitude of electric field?

The unit of measurement for the magnitude of electric field is newtons per coulomb (N/C) in the SI system of units.

4. How does distance affect the magnitude of electric field?

The magnitude of electric field is inversely proportional to the square of the distance between the source of the field and the point of measurement. This means that as distance increases, the magnitude of electric field decreases.

5. Can the magnitude of electric field be negative?

Yes, the magnitude of electric field can be negative. This occurs when the direction of the electric force on a positive test charge is opposite to the direction of the electric field.

Similar threads

  • Advanced Physics Homework Help
Replies
4
Views
3K
  • Advanced Physics Homework Help
Replies
4
Views
2K
  • Advanced Physics Homework Help
Replies
2
Views
3K
  • Advanced Physics Homework Help
Replies
2
Views
1K
  • Advanced Physics Homework Help
Replies
26
Views
4K
  • Advanced Physics Homework Help
Replies
2
Views
1K
  • Advanced Physics Homework Help
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
17
Views
323
  • Advanced Physics Homework Help
Replies
7
Views
1K
  • Introductory Physics Homework Help
Replies
9
Views
676
Back
Top