- #1
phisci
- 10
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Hi all, I need your help with a question. Here goes,
There is a hollow conducting sphere with a uniform surface charge density of +[tex]\sigma[/tex]. A charge -q, is placed inside the cavity of the hollow sphere. What is the electric flux through a spherical surface just inside the inner surface of the sphere?
Gaussian sphere.
From my understanding, for a conductor with uniform surface charge density, there is no electric field inside the conductor, assuming electrostatic situation. When a charge -q is placed inside the cavity of the hollow sphere, it will induce positive charges amounting to +q around the cavity to cancel out the effect of -q and hence the net electric field within the conductor is zero. If I consider a Gaussian sphere just inside the inner surface of the sphere, due to symmetrical properties of the sphere, the electric flux [tex]\phi[/tex]= Qenc/[tex]\epsilon[/tex]Since the enclosed net charge is the charge -q and the induced charge around the cavity is +q, the net Qenc is 0, hence the electric flux is 0.
However the answer to this question is q/[tex]\epsilon[/tex] Where have I gone wrong in my reasoning? Thank you so much!
Sorry if the post seems messy, I'm not too sure how to post the Greek Symbols with the subscripts. The 0 should be a subscript 0 for epsilon. My apologies again.
Homework Statement
There is a hollow conducting sphere with a uniform surface charge density of +[tex]\sigma[/tex]. A charge -q, is placed inside the cavity of the hollow sphere. What is the electric flux through a spherical surface just inside the inner surface of the sphere?
Homework Equations
Gaussian sphere.
The Attempt at a Solution
From my understanding, for a conductor with uniform surface charge density, there is no electric field inside the conductor, assuming electrostatic situation. When a charge -q is placed inside the cavity of the hollow sphere, it will induce positive charges amounting to +q around the cavity to cancel out the effect of -q and hence the net electric field within the conductor is zero. If I consider a Gaussian sphere just inside the inner surface of the sphere, due to symmetrical properties of the sphere, the electric flux [tex]\phi[/tex]= Qenc/[tex]\epsilon[/tex]Since the enclosed net charge is the charge -q and the induced charge around the cavity is +q, the net Qenc is 0, hence the electric flux is 0.
However the answer to this question is q/[tex]\epsilon[/tex] Where have I gone wrong in my reasoning? Thank you so much!
Sorry if the post seems messy, I'm not too sure how to post the Greek Symbols with the subscripts. The 0 should be a subscript 0 for epsilon. My apologies again.