Where Inside an Insulating Sphere is the Electric Field Zero?

In summary, an insulating sphere with a radius of 0.120 m and a charge of 0.750 nC distributed throughout its volume is placed 0.240 m above a large sheet with a charge density of -9.40 nC/m2. The goal is to find all points inside the sphere where the electric field is zero. Using the integral equation and the superposition principle, the electric fields for just the charged sphere and just the charged sheet were calculated. To find the combined field, the vector sum of the two individual fields needs to be taken into account.
  • #1
Clement
6
0

Homework Statement



An insulating sphere with radius 0.120 m has 0.750 nC of charge uniformly distributed throughout its volume. The center of the sphere is 0.240 m above a large uniform sheet that has charge density -9.40 nC/m2. Find all points inside the sphere where the electric field is zero.

Homework Equations



Intergral(E da) = Q_enclosed/epsilon_0

3. The Attempt at a Solution [/b
I drew the picture, but I don't know where to start.
 
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  • #2
(1)If you had just the charged sphere and no charged sheet could you find the electric field?

(2)If you had just the charged sheet, and no sphere could you find the field?

(3)What does the superposition principle tell you about the combined field of the two objects?:wink:
 
  • #3
(1)I think so, the electric field inside the sphere is (kQr)/R^3

(2)E= sigma/(2epsilon_0)

(3)sigma/(2epsilon_0)+(kQr)/R^3=0?

got it, thank you so much!
 
  • #4
Careful, the fields are both vectors, so for (3) you need the vector sum of the two individual fields to be zero...you need to take the direction of each field into account.
 

FAQ: Where Inside an Insulating Sphere is the Electric Field Zero?

What is Gauss's Law and how is it related to electric field?

Gauss's Law is a fundamental law in electromagnetism that relates the electric flux through a closed surface to the charge enclosed by that surface. It states that the electric flux through any closed surface is proportional to the total charge enclosed by that surface. This law is closely related to the concept of electric field, as the flux through a surface is directly related to the electric field passing through that surface.

What is the formula for Gauss's Law?

The mathematical representation of Gauss's Law is given by the equation ∮S E * dA = Qenc/ε0, where ∮S E * dA represents the electric flux through a closed surface S, Qenc is the total charge enclosed by that surface, and ε0 is the permittivity of free space. This equation is known as the integral form of Gauss's Law.

What is the significance of Gauss's Law in electromagnetism?

Gauss's Law is one of the four Maxwell's equations, which form the basis of classical electromagnetism. It is an important tool for studying the behavior of electric fields and charges, and is used extensively in many areas of physics and engineering, including circuit analysis, electromagnetics, and optics.

How is Gauss's Law applied in real-life situations?

Gauss's Law has many practical applications, such as in the design of electronic circuits and in the development of devices such as capacitors and electric motors. It is also used in the study of lightning and electrical discharges, and is essential for understanding the behavior of electromagnetic waves.

What are some common misconceptions about Gauss's Law?

One common misconception is that Gauss's Law only applies to simple, symmetric geometries. In reality, it can be applied to any closed surface, regardless of its shape or orientation. Another misconception is that Gauss's Law only applies to static electric fields. In fact, it can also be used to analyze time-varying electric fields, as long as the displacement current is taken into account. Additionally, Gauss's Law does not determine the direction of the electric field itself, but rather the net flux through a surface due to all sources of electric charge.

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