Question 804: Electrostatics & Capacitance

Question

Consider a thin spherical shell of radius $$R$$ with center at the origin, carrying uniform positive surface charge density. The variation of the magnitude of the electric field $$\left| {\overrightarrow E \left( r \right)} \right|$$ and the electric potential $$V(r)$$ with the distance $$r$$ from the center, best represented by which graph?

Accepted Answer

Consider a thin spherical shell of radius $ R $ with its center at the origin, carrying a uniform positive surface charge density. To understand how the electric field $ \left| \overrightarrow{E} \left( r ight) ight| $ and the electric potential $ V(r) $ vary with the distance $ r $ from the center, refer to the following details:
Electric Field due to a Uniformly Charged Thin Spherical Shell
Inside the Shell
For $ r  R $, the electric field is:
$$ E_{	ext{outside}} = \frac{1}{4 \pi \varepsilon_0} \frac{Q}{r^2} \quad [ r > R ] $$
Below is a graphical representation of the electric field $ E $ variation with the distance $ r $ from the center:
Electric Potential due to a Uniformly Charged Thin Spherical Shell
Inside the Shell
For $ r  R $, the electric potential is:
$$ V_{	ext{outside}} = \frac{1}{4 \pi \varepsilon_0} \frac{Q}{r} $$
Below is a graphical representation of the electric potential $ V $ variation with the distance $ r $ from the center:

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Electrostatics & Capacitance

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