Question 187: Electrostats & Capacitance

Question

A spherical portion has been removed from a solid sphere having a charge distributed uniformly in its volume as shown in the figure. The electric field inside the emptied space is

Accepted Answer

When cavity is not present:
Electric field inside the solid sphere
$$
\overrightarrow{\mathrm{E}_{1}}=\frac{ho}{3 \varepsilon_{0}} \overrightarrow{r_{1}}
$$ ..... (i)
Solid sphere after making cavity inside solid sphere,
$$
\overrightarrow{\mathrm{E}_{2}}=\frac{ho}{3 \varepsilon_{0}} \overrightarrow{r_{2}}
$$ ...... (ii)
$${\overrightarrow E _{net}} = \overrightarrow {{E_1}}  - \overrightarrow {{E_2}}  = {ho  \over {3{\varepsilon _0}}}\overrightarrow {{r_1}}  - {ho  \over {3{\varepsilon _0}}}\overrightarrow {{r_2}} $$
$$=\frac{ho}{3 \varepsilon_{0}}\left(\overrightarrow{r_{1}}-\overrightarrow{r_{2}}ight)
$$ ...... (iii)
From eq (iii), we get
$$	herefore \quad \mathrm{E}_{\mathrm{net}}=\frac{ho}{3 \varepsilon_{0}}(\vec{r})$$
Hence, electric field inside the emptied space (cavity) is non-zero and uniform.

Answer

zero everywhere

Answer

non-zero and uniform

Answer

non-uniform

Answer

zero only at its center

Electrostats & Capacitance

A spherical portion has been removed from a solid sphere having a charge distributed uniformly in its volume as shown in the figure. The electric field inside the emptied space is

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