Where Inside an Insulating Sphere is the Electric Field Zero?

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SUMMARY

The discussion focuses on determining the points inside an insulating sphere where the electric field is zero, given a uniformly charged sphere with a radius of 0.120 m and a charge of 0.750 nC, positioned above a charged sheet with a density of -9.40 nC/m². The solution involves applying the superposition principle to combine the electric fields from both the sphere and the sheet. The electric field inside the sphere is calculated using the formula E = (kQr)/R³, while the field from the sheet is E = σ/(2ε₀). The key conclusion is that the vector sum of these fields must equal zero for specific points within the sphere.

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  • Familiarity with Gauss's Law and its applications
  • Knowledge of the superposition principle in electrostatics
  • Basic concepts of charge distribution and density
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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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(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:
 
(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!
 
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.
 

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