Using thomson's model of atom, consider an atom consisting of two electrons, each of charge -e ,

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1. Electric Charges and Fields

hard

Using thomson's model of the atom, consider an atom consisting of two electrons, each of charge $-e$, embeded in a sphere of charge $+2e$ and radius $R$. In equilibrium each electron is at a distance $d$ from the centre of the atom. What is the equilibrium separation between electrons

$R$

$\frac{R}{2}$

$\frac{R}{3}$

$\frac{R}{4}$

Solution

Considering gaussian surface

$\phi=\frac{q_{\text {in }}}{\varepsilon_{0}} \Rightarrow E 4 \pi d^{2}=\frac{2 e d^{3}}{\varepsilon_{0} R^{3}}$

$\mathrm{E}=\frac{2 \mathrm{edk}}{\mathrm{R}^{3}}$

For equilibrium of charge,

$\frac{\text { kee }}{(2 d)^{2}}=\left(\frac{\text { k } 2 \text { ed }}{R^{3}}\right) e$

$\frac{1}{4 \mathrm{d}^{2}}=\frac{2 \mathrm{d}}{\mathrm{R}^{3}} \Rightarrow \mathrm{d}^{3}=\frac{\mathrm{R}^{3}}{8} \Rightarrow \mathrm{d}=\mathrm{R} / 2$

Standard 12

Physics

It is not convenient to use a spherical Gaussian surface to find the electric field due to an electric dipole using Gauss’s theorem because

easy

Two surfaces $S_1$ and $S_2$ are shown in figure. Flux associated with $S_1$ is ${\phi _1}$ and $S_2$ is ${\phi _2}$. Which is correct ?

easy

Assertion : Four point charges $q_1,$ $q_2$, $q_3$ and $q_4$ are as shown in figure. The flux over the shown Gaussian surface depends only on charges $q_1$ and $q_2$.

Reason : Electric field at all points on Gaussian surface depends only on charges $q_1$ and $q_2$ .

easy

(AIIMS-2012)

A long cylindrical volume contains a uniformly distributed charge of density $\rho \;Cm ^{-3}$. The electric field inside the cylindrical volume at a distance $x =\frac{2 \varepsilon_{0}}{\rho} m$ from its axis is $…….Vm ^{-1}$

hard

(JEE MAIN-2022)

A point charge $q$ is placed at a distance $a/2$ directly above the centre of a square of side $a$. The electric flux through the square is

easy

Using thomson's model of the atom, consider an atom consisting of two electrons, each of charge $-e$, embeded in a sphere of charge $+2e$ and radius $R$. In equilibrium each electron is at a distance $d$ from the centre of the atom. What is the equilibrium separation between electrons

Solution

Similar Questions

It is not convenient to use a spherical Gaussian surface to find the electric field due to an electric dipole using Gauss’s theorem because

Two surfaces $S_1$ and $S_2$ are shown in figure. Flux associated with $S_1$ is ${\phi _1}$ and $S_2$ is ${\phi _2}$. Which is correct ?

Assertion : Four point charges $q_1,$ $q_2$, $q_3$ and $q_4$ are as shown in figure. The flux over the shown Gaussian surface depends only on charges $q_1$ and $q_2$. Reason : Electric field at all points on Gaussian surface depends only on charges $q_1$ and $q_2$ .

A long cylindrical volume contains a uniformly distributed charge of density $\rho \;Cm ^{-3}$. The electric field inside the cylindrical volume at a distance $x =\frac{2 \varepsilon_{0}}{\rho} m$ from its axis is $…….Vm ^{-1}$

A point charge $q$ is placed at a distance $a/2$ directly above the centre of a square of side $a$. The electric flux through the square is

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Assertion : Four point charges $q_1,$ $q_2$, $q_3$ and $q_4$ are as shown in figure. The flux over the shown Gaussian surface depends only on charges $q_1$ and $q_2$.

Reason : Electric field at all points on Gaussian surface depends only on charges $q_1$ and $q_2$ .