A paisa coin is made up of $\mathrm{Al - Mg}$ alloy and weighs $0.75\, g$ It is electrically neutral and contains equal amounts of positive and negative charge of magnitude $34.8$ $\mathrm{kC}$. Suppose that these equal charges were concentrated in two point charges separated by :
$(i)$ $1$ $\mathrm{cm}$ $(\sim \frac{1}{2} \times $ diagonal of the one paisa coin $)$
$(ii)$ $100\,\mathrm{m}$ $(\sim $ length of a long building $)$
$(iii)$ $10^6$ $\mathrm{m}$ (radius of the earth).
Find the force on each such point charge in each of the three cases. What do you conclude from these results ?
A paisa coin is made up of $\mathrm{Al - Mg}$ alloy and weighs $0.75\, g$ It is electrically neutral and contains equal amounts of positive and negative charge of magnitude $34.8$ $\mathrm{kC}$. Suppose that these equal charges were concentrated in two point charges separated by :
$(i)$ $1$ $\mathrm{cm}$ $(\sim \frac{1}{2} \times $ diagonal of the one paisa coin $)$
$(ii)$ $100\,\mathrm{m}$ $(\sim $ length of a long building $)$
$(iii)$ $10^6$ $\mathrm{m}$ (radius of the earth).
Find the force on each such point charge in each of the three cases. What do you conclude from these results ?
Here, $r_{1}=1 \mathrm{~cm}=10^{-2} \mathrm{~m}$
$r_{2}=100 \mathrm{~m}$ $r_{3}=10^{6} \mathrm{~m}$ $\frac{1}{4 \pi \epsilon_{0}}=k=9 \times 10^{9}$
$(i)$ $\mathrm{F}_{1}=\frac{k|q|^{2}}{r_{1}^{2}}=\frac{9 \times 10^{9} \times\left(3.48 \times 10^{4}\right)^{2}}{\left(10^{-2}\right)^{2}}=1.0899 \times 10^{23} \mathrm{~N}$ $=1.09 \times 10^{23} \mathrm{~N}$
$(ii)$ $\mathrm{F}_{2}=\frac{k|q|^{2}}{r_{2}^{2}}=\frac{9 \times 10^{9} \times\left(3.48 \times 10^{4}\right)^{2}}{(100)^{2}}=1.09 \times 10^{15} \mathrm{~N}$
$(iii)$ $\mathrm{F}_{3}=\frac{k|q|^{2}}{r_{3}^{2}}=\frac{9 \times 10^{9} \times\left(3.48 \times 10^{4}\right)^{2}}{\left(10^{6}\right)^{2}}=1.09 \times 10^{7} \mathrm{~N}$
Here, the force between charges is much more hence, it is difficult to disturb electrical neutrality of matter.
Similar Questions
The ratio of coulomb's electrostatic force to the gravitational force between an electron and a proton separated by some distance is $2.4 \times 10^{39}$. The ratio of the proportionality constant, $K=\frac{1}{4 \pi \varepsilon_0}$ to the Gravitational constant $G$ is nearly (Given that the charge of the proton and electron each $=1.6 \times 10^{-19}\; C$, the mass of the electron $=9.11 \times 10^{-31}\; kg$, the mass of the proton $=1.67 \times 10^{-27}\,kg$ ):
The ratio of coulomb's electrostatic force to the gravitational force between an electron and a proton separated by some distance is $2.4 \times 10^{39}$. The ratio of the proportionality constant, $K=\frac{1}{4 \pi \varepsilon_0}$ to the Gravitational constant $G$ is nearly (Given that the charge of the proton and electron each $=1.6 \times 10^{-19}\; C$, the mass of the electron $=9.11 \times 10^{-31}\; kg$, the mass of the proton $=1.67 \times 10^{-27}\,kg$ ):
- [NEET 2022]
Write limitation of Coulomb’s law.
Write limitation of Coulomb’s law.
Two electrons are separated by a distance of $1\,\mathop A\limits^o $. What is the coulomb force between them
Two electrons are separated by a distance of $1\,\mathop A\limits^o $. What is the coulomb force between them
Select the correct alternative
Select the correct alternative
A particle of charge $-q$ and mass $m$ moves in a circle of radius $r$ around an infinitely long line charge of linear density $+\lambda$. Then time period will be given as
(Consider $k$ as Coulomb's constant)
A particle of charge $-q$ and mass $m$ moves in a circle of radius $r$ around an infinitely long line charge of linear density $+\lambda$. Then time period will be given as
(Consider $k$ as Coulomb's constant)
- [JEE MAIN 2024]