A spherical portion has been removed from a s | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Consider a solid sphere of radius $R$ with uniform charge density $\rho$. Let the center of the large sphere be at the origin $O_1$ and the center

Vedclass · Accepted Answer

non-zero and uniform

Vedclass · Answer

(B) Consider a solid sphere of radius $R$ with uniform charge density $\rho$. Let the center of the large sphere be at the origin $O_1$ and the center of the removed spherical cavity be at $O_2$. Let $\vec{a}$ be the position vector of $O_2$ relative to $O_1$.The electric field at any point $P$ inside the cavity can be calculated using the principle of superposition. We can treat the system as a large positively charged sphere and a smaller negatively charged sphere (the cavity) superimposed on it.The electric field due to the large sphere at point $P$ (position vector $\vec{r}_1$ from $O_1$) is $\vec{E}_1 = \frac{\rho \vec{r}_1}{3 \epsilon_0}$.The electric field due to the smaller sphere (cavity) at point $P$ (position vector $\vec{r}_2$ from $O_2$) is $\vec{E}_2 = -\frac{\rho \vec{r}_2}{3 \epsilon_0}$.The net electric field $\vec{E}$ at point $P$ is $\vec{E} = \vec{E}_1 + \vec{E}_2 = \frac{\rho}{3 \epsilon_0} (\vec{r}_1 - \vec{r}_2)$.Since $\vec{r}_1 = \vec{a} + \vec{r}_2$,we have $\vec{r}_1 - \vec{r}_2 = \vec{a}$.Thus,$\vec{E} = \frac{\rho \vec{a}}{3 \epsilon_0}$.Since $\rho$,$\vec{a}$,and $\epsilon_0$ are constants,the electric field inside the cavity is non-zero and uniform.

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

Similar Questions

Which tissue is mainly composed of fat-storing cells?

Let $\alpha$ and $\beta$ be the roots of the equation $x^2-x-1=0$. If $p_{k}=(\alpha)^{k}+(\beta)^{k}, k \geq 1$,then which one of the following statements is not true?

Which of the following is arranged in decreasing order of size?

Which of the following have sunken stomata?

Vedclass Test Series

Exam Paper Generator

Online Exam Module