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]
- A
$9$
- B
$16$
- C
$12$
- D
$24$
Similar Questions
The ratio of electrostatic and gravitational forces acting between electron and proton separated by a distance $5 \times {10^{ - 11}}\,m,$ will be (Charge on electron $=$ $1.6 \times 10^{-19}$ $C$, mass of electron = $ 9.1 \times 10^{-31}$ $kg$, mass of proton = $1.6 \times {10^{ - 27}}\,kg,$ $\,G = 6.7 \times {10^{ - 11}}\,N{m^2}/k{g^2})$
The ratio of electrostatic and gravitational forces acting between electron and proton separated by a distance $5 \times {10^{ - 11}}\,m,$ will be (Charge on electron $=$ $1.6 \times 10^{-19}$ $C$, mass of electron = $ 9.1 \times 10^{-31}$ $kg$, mass of proton = $1.6 \times {10^{ - 27}}\,kg,$ $\,G = 6.7 \times {10^{ - 11}}\,N{m^2}/k{g^2})$
$ + 2\,C$ and $ + 6\,C$ two charges are repelling each other with a force of $12\,N$. If each charge is given $ - 2\,C$ of charge, then the value of the force will be
$ + 2\,C$ and $ + 6\,C$ two charges are repelling each other with a force of $12\,N$. If each charge is given $ - 2\,C$ of charge, then the value of the force will be
The diagrams depict four different charge distributions. All the charged particles are at same distance from origin $(i.e. OA = OB = OC = OD)$ $F_1$ , $F_2$ , $F_3$ and $F_4$ are the magnitude of electrostatic force experienced by a point charge $q_0$ kept at origin in figure $-1$ , figure $-2$ , figure $-3$ and figure $-4$ respectively. Choose the correct statement.
The diagrams depict four different charge distributions. All the charged particles are at same distance from origin $(i.e. OA = OB = OC = OD)$ $F_1$ , $F_2$ , $F_3$ and $F_4$ are the magnitude of electrostatic force experienced by a point charge $q_0$ kept at origin in figure $-1$ , figure $-2$ , figure $-3$ and figure $-4$ respectively. Choose the correct statement.
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 ?
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 ?