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 law, governing the force between electric charges is known as
The law, governing the force between electric charges is known as
Two identical tennis balls each having mass $m$ and charge $q$ are suspended from a fixed point by threads of length $l$. What is the equilibrium separation when each thread makes a small angle $\theta$ with the vertical?
Two identical tennis balls each having mass $m$ and charge $q$ are suspended from a fixed point by threads of length $l$. What is the equilibrium separation when each thread makes a small angle $\theta$ with the vertical?
- [JEE MAIN 2021]
Three identical charged balls each of charge $2 \,C$ are suspended from a common point $P$ by silk threads of $2 \,m$ each (as shown in figure). They form an equilateral triangle of side $1 \,m$.
The ratio of net force on a charged ball to the force between any two charged balls will be ...........
Three identical charged balls each of charge $2 \,C$ are suspended from a common point $P$ by silk threads of $2 \,m$ each (as shown in figure). They form an equilateral triangle of side $1 \,m$.
The ratio of net force on a charged ball to the force between any two charged balls will be ...........
- [JEE MAIN 2022]
An infinite number of point charges, each carrying $1 \,\mu C$ charge, are placed along the y-axis at $y=1\, m , 2\, m , 4 \,m , 8\, m \ldots \ldots \ldots \ldots \ldots$
The total force on a $1 \,C$ point charge, placed at the origin, is $x \times 10^{3}\, N$. The value of $x$, to the nearest integer, is .........
[Take $\left.\frac{1}{4 \pi \epsilon_{0}}=9 \times 10^{9} \,Nm ^{2} / C ^{2}\right]$
An infinite number of point charges, each carrying $1 \,\mu C$ charge, are placed along the y-axis at $y=1\, m , 2\, m , 4 \,m , 8\, m \ldots \ldots \ldots \ldots \ldots$
The total force on a $1 \,C$ point charge, placed at the origin, is $x \times 10^{3}\, N$. The value of $x$, to the nearest integer, is .........
[Take $\left.\frac{1}{4 \pi \epsilon_{0}}=9 \times 10^{9} \,Nm ^{2} / C ^{2}\right]$
- [JEE MAIN 2021]
Three charge $q$, $Q$ and $4q$ are placed in a straight line of length $l$ at points distant $0,\,\frac {l}{2}$ and $l$ respectively from one end. In order to make the net froce on $q$ zero, the charge $Q$ must be equal to
Three charge $q$, $Q$ and $4q$ are placed in a straight line of length $l$ at points distant $0,\,\frac {l}{2}$ and $l$ respectively from one end. In order to make the net froce on $q$ zero, the charge $Q$ must be equal to