Question

From a given sphere of radius $R$ wiht uniform positive charge density $\rho$, a smaller sphere of radius $\frac{R}{2}$ it carved out as shown in figure. If electric field at points $A$ and $B$ are ${\overrightarrow{E}}_A$ and ${\overrightarrow{E}}_B$ respectively, then

Diagram

• A. $\overrightarrow{B}=\frac{17}{54}\frac{\rho R}{{\epsilon }_0}(-\hat{i})$
• B. Direction of field changes from $A$ and $B$
• C. Direction of electric field remaisn unchanged from $A$ and $B$
• D. ${\overrightarrow{E}}_A=\frac{\rho R}{6{\epsilon }_0}\hat{i}$

Answer 1

Answer: (A), (B), (D)

${\overrightarrow{E}}_A=\frac{\rho R}{6{\epsilon }_0}\hat{i}$

${\overrightarrow{E}}_A={\overrightarrow{E}}_{sphere}+{\overrightarrow{E}}_{cavity}$
${\overrightarrow{E}}_A=0+\frac{\rho R}{6{\epsilon }_0}(+\hat{j})$
${\overrightarrow{E}}_B=-\frac{rhoR}{3{\epsilon }_0}\left(\hat{i}\right)+\frac{\rho R(+\hat{i})}{54{\epsilon }_0}=-\frac{17\rho R}{54{\epsilon }_0}$