$(a)$ Two insulated charged copper spheres $A$ and $B$ have their centres separated by a distance of $50 \;cm$. What is the mutual force of electrostatic repulsion if the charge on each is $6.5 \times 10^{-7}\; C?$ The radii of $A$ and $B$ are negligible compared to the distance of separation.
$(b)$ What is the force of repulsion if each sphere is charged double the above amount, and the distance between them is halved?
$(a)$ Two insulated charged copper spheres $A$ and $B$ have their centres separated by a distance of $50 \;cm$. What is the mutual force of electrostatic repulsion if the charge on each is $6.5 \times 10^{-7}\; C?$ The radii of $A$ and $B$ are negligible compared to the distance of separation.
$(b)$ What is the force of repulsion if each sphere is charged double the above amount, and the distance between them is halved?
$(a)$ Charge on sphere $A , q _{ A }=6.5 \times 10^{-7}\, C$
Charge on sphere $B , q _{ B }=6.5 \times 10^{-7} \,C$
Distance between the spheres, $r=50 \,cm =0.5 \,m$ Force of repulsion between the two spheres
$F=\frac{1}{4 \pi \varepsilon_{0}} \cdot \frac{q_{A} q_{B}}{r^{2}}$
Where, $\varepsilon_{0}=$ Permittivity of free space and $\frac{1}{4 \pi \varepsilon_{0}}=9 \times 10^{9} \,Nm ^{2} \,C ^{-2}$
Therefore,
$F =\frac{9 \times 10^{9} \times\left(6.5 \times 10^{-7}\right)^{2}}{(0.5)^{2}}$
$=1.52 \times 10^{-2} \,N$
Therefore, the force between the two spheres is $1.52 \times 10^{-2} \,N$
$(b)$ After doubling the charge, Charge on sphere $A , q _{ A }=1.3 \times 10^{-6} \,C$
Charge on sphere $B , q _{ B }=1.3 \times 10^{-6} \,C$
The distance between the spheres is halved.
$\therefore r=\frac{0.5}{2}=0.25\, m$
Force of repulsion between the two spheres,
$F=\frac{1}{4 \pi \varepsilon_{0}} \cdot \frac{q_{A} q_{B}}{r^{2}}$$=\frac{9 \times 10^{9} \times 1.3 \times 10^{-6} \times 1.3 \times 10^{-6}}{(0.25)^{2}}$
$=16 \times 1.52 \times 10^{-2}$
$=0.243 \,N$
Therefore, the force between the two spheres is $0.243 \,N$.
Similar Questions
Three points charges are placed at the corners of an equilateral triangle of side $L$ as shown in the figure.
Three points charges are placed at the corners of an equilateral triangle of side $L$ as shown in the figure.
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 ?
Explain the superposition principle for static electric forces and write its general equation.
Explain the superposition principle for static electric forces and write its general equation.
Two fixed charges $4\,Q$ (positive) and $Q$ (negative) are located at $A$ and $B$, the distance $AB$ being $3$ $m$.
Two fixed charges $4\,Q$ (positive) and $Q$ (negative) are located at $A$ and $B$, the distance $AB$ being $3$ $m$.
Four point $+ve$ charges of same magnitude $(Q)$ are placed at four corners of a rigid square frame as shown in figure. The plane of the frame is perpendicular to $Z$ axis. If a $-ve$ point charge is placed at a distance $z$ away from the above frame $(z<< L)$ then
Four point $+ve$ charges of same magnitude $(Q)$ are placed at four corners of a rigid square frame as shown in figure. The plane of the frame is perpendicular to $Z$ axis. If a $-ve$ point charge is placed at a distance $z$ away from the above frame $(z<< L)$ then
- [AIIMS 2005]