Question
A hollow conducting sphere of radius $R$ carries a negative charge $-q .$ (a) Write expressions for the electric field $\overrightarrow{\mathbf{E}}$ inside $(r<R)$ and outside $(r>R)$ the sphere. Also indicate the direction of the field.(b) Sketch a graph of the field strength as a function of $r .[$Hint: See Conceptual Example 16.8 .1
Step 1
This is because the charges in a conductor rearrange themselves in such a way that the electric field inside the conductor is zero. Therefore, for $r<R$, we have: \[\overrightarrow{\mathbf{E}} = 0\] Show more…
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A hollow conducting sphere of radius $R$ carries a negative charge $-q .$ (a) Write expressions for the electric field $\overrightarrow{\mathbf{E}}$ inside $(r<R)$ and outside $(r>R)$ the sphere. Also indicate the direction of the field. (b) Sketch a graph of the field strength as a function of $r$. [Hint: See Conceptual Example $16.8 .]$
A solid conducting sphere carrying charge q has radius a. It is inside a concentric hollow conducting sphere with inner radius b and outer radius c with a < b < c. The hollow sphere has no net charge. (a) Derive expressions for the electric-field magnitude in terms of the distance r from the center for the regions r < a, a < r < b, b < r < c, and r > c. (b) Graph the magnitude of the electric field as a function of r from r = 0 to r = 2c. (c) What is the charge on the inner surface of the hollow sphere? (d) What is the charge on the outer surface of the hollow sphere?
A solid conducting sphere carrying charge $q$ has radius $a$. It is inside a concentric hollow conducting sphere with inner radius $b$ and outer radius $c .$ The hollow sphere has no net charge. (a) Derive expressions for the electric-field magnitude in terms of the distance $r$ from the center for the regions $r<a$, $a<r<b, b<r<c,$ and $r>c .$ (b) Graph the magnitude of the electric field as a function of $r$ from $r=0$ to $r=2 c$. (c) What is the charge on the inner surface of the hollow sphere? (d) On the outer surface? (e) Represent the charge of the small sphere by four plus signs. Sketch the field lines of the system within a spherical volume of radius $2 c$.
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