Figure represents a crystal unit of cesium chloride, $\mathrm{CsCl}$. The cesium atoms, represented by open circles are situated at the corners of a cube of side $0.40\,\mathrm{nm}$, whereas a $\mathrm{Cl}$ atom is situated at the centre of the cube. The $\mathrm{Cs}$ atoms are deficient in one electron while the $\mathrm{Cl}$ atom carries an excess electron.
$(i)$ What is the net electric field on the $\mathrm{Cl}$ atom due to eight $\mathrm{Cs}$ atoms ?
$(ii)$ Suppose that the $\mathrm{Cs}$ atom at the corner $A$ is missing. What is the net force now on the $\mathrm{Cl}$ atom due to seven remaining $\mathrm{Cs}$ atoms ?
Figure represents a crystal unit of cesium chloride, $\mathrm{CsCl}$. The cesium atoms, represented by open circles are situated at the corners of a cube of side $0.40\,\mathrm{nm}$, whereas a $\mathrm{Cl}$ atom is situated at the centre of the cube. The $\mathrm{Cs}$ atoms are deficient in one electron while the $\mathrm{Cl}$ atom carries an excess electron.
$(i)$ What is the net electric field on the $\mathrm{Cl}$ atom due to eight $\mathrm{Cs}$ atoms ?
$(ii)$ Suppose that the $\mathrm{Cs}$ atom at the corner $A$ is missing. What is the net force now on the $\mathrm{Cl}$ atom due to seven remaining $\mathrm{Cs}$ atoms ?
$(i)$ The cesium atoms are situated at the corners of a cube and $\mathrm{CI}$ atom is situated at the centre of the cube. From the given figure, we can analyses that the chlorine atom is at equal distance from all the eight corners of cube where cesium atoms are placed. Thus, due to symmetry the electric field due to all $\mathrm{Cs}$ atoms, on $\mathrm{Cl}$ atom will cancel out.
Hence $E=\frac{F}{q}, F=0$
$(ii)$ We define force on a charge particle due to external electric field as $\mathrm{F}=q \mathrm{E}$. If eight cesium atoms are situated at the corners of a cube, the net force on $\mathrm{Cl}$ atom is situated at the centre of the cube will be zero as net electric field at the centre of cube is zero. But, force acting on $\mathrm{Cl}^{-}$ion by each $\mathrm{Cs}^{+}$ion,
$\mathrm{F}=\frac{k e^{2}}{r^{2}} \quad \ldots \text { (1) }$
From Pythagoras theorem,
$r=\sqrt{\left(0.2 \times 10^{-9}\right)^{2}+\left(0.2 \times 10^{-9}\right)^{2}+\left(0.2 \times 10^{-9}\right)^{2}}$
$=\sqrt{4+4+4} \times 10^{-10}$
$=\sqrt{12} \times 10^{-10}$
$=3.46 \times 10^{-10} \mathrm{~m}$
$\therefore \text { From equation (1), }$
$\qquad$
$\mathrm{F} =\frac{9 \times 10^{9} \times\left(1.6 \times 10^{-19}\right)^{2}}{\left(3.46 \times 10^{-10}\right)^{2}}$
$\therefore \mathrm{F} =1.92 \times 10^{-9} \mathrm{~N}$
Similar Questions
For regular pentagon system shown in figure, find force on $q_0$
For regular pentagon system shown in figure, find force on $q_0$
A thin metallic wire having cross sectional area of $10^{-4} \mathrm{~m}^2$ is used to make a ring of radius $30 \mathrm{~cm}$. A positive charge of $2 \pi \mathrm{C}$ is uniformly distributed over the ring, while another positive charge of $30$ $\mathrm{pC}$ is kept at the centre of the ring. The tension in the ring is__________ $\mathrm{N}$; provided that the ring does not get deformed (neglect the influence of gravity). (given, $\frac{1}{4 \pi \epsilon_0}=9 \times 10^9 \mathrm{SI}$ units)
A thin metallic wire having cross sectional area of $10^{-4} \mathrm{~m}^2$ is used to make a ring of radius $30 \mathrm{~cm}$. A positive charge of $2 \pi \mathrm{C}$ is uniformly distributed over the ring, while another positive charge of $30$ $\mathrm{pC}$ is kept at the centre of the ring. The tension in the ring is__________ $\mathrm{N}$; provided that the ring does not get deformed (neglect the influence of gravity). (given, $\frac{1}{4 \pi \epsilon_0}=9 \times 10^9 \mathrm{SI}$ units)
- [JEE MAIN 2024]
Two identical positive charges $Q$ each are fixed at a distance of ' $2 a$ ' apart from each other. Another point charge qo with mass ' $m$ ' is placed at midpoint between two fixed charges. For a small displacement along the line joining the fixed charges, the charge $q_{0}$ executes $SHM$. The time period of oscillation of charge $q_{0}$ will be.
Two identical positive charges $Q$ each are fixed at a distance of ' $2 a$ ' apart from each other. Another point charge qo with mass ' $m$ ' is placed at midpoint between two fixed charges. For a small displacement along the line joining the fixed charges, the charge $q_{0}$ executes $SHM$. The time period of oscillation of charge $q_{0}$ will be.
- [JEE MAIN 2022]
Two identical metallic spheres $A$ and $B$ when placed at certain distance in air repel each other with a force of $F$. Another identical uncharged sphere $C$ is first placed in contact with $A$ and then in contact with $B$ and finally placed at midpoint between spheres $A$ and $B$. The force experienced by sphere $C$ will be.
Two identical metallic spheres $A$ and $B$ when placed at certain distance in air repel each other with a force of $F$. Another identical uncharged sphere $C$ is first placed in contact with $A$ and then in contact with $B$ and finally placed at midpoint between spheres $A$ and $B$. The force experienced by sphere $C$ will be.
- [JEE MAIN 2022]
Two equally charged, identical metal spheres $A$ and $B$ repel each other with a force '$F$'. The spheres are kept fixed with a distance '$r$' between them. A third identical, but uncharged sphere $C$ is brought in contact with $A$ and then placed at the mid-point of the line joining $A$ and $B$. The magnitude of the net electric force on $C$ is
Two equally charged, identical metal spheres $A$ and $B$ repel each other with a force '$F$'. The spheres are kept fixed with a distance '$r$' between them. A third identical, but uncharged sphere $C$ is brought in contact with $A$ and then placed at the mid-point of the line joining $A$ and $B$. The magnitude of the net electric force on $C$ is