Consider three charges $q_{1}, q_{2}, q_{3}$ each equal to $q$ at the vertices of an equilateral triangle of side $l .$ What is the force on a charge $Q$ (with the same sign as $q$ ) placed at the centroid of the triangle, as shown in Figure
Consider three charges $q_{1}, q_{2}, q_{3}$ each equal to $q$ at the vertices of an equilateral triangle of side $l .$ What is the force on a charge $Q$ (with the same sign as $q$ ) placed at the centroid of the triangle, as shown in Figure
In the given equilateral triangle $ABC$ of sides of length $l$, if Iraw a perpendicular $AD$ to the side $BC,$
$A D=A C \cos 30^{\circ}=(\sqrt{3} / 2) l$ and the distance $AO$ of the centroid $O$ from $A$ is $(2 / 3) AD =(1 / \sqrt{3})$ $l$. By symmatry $AO = BO = CO$
Thus,
Force $F _{1}$ on $Q$ due to charge $q$ at $A =\frac{3}{4 \pi \varepsilon_{0}} \frac{ Q q}{l^{2}}$ along $AO$
Force $F _{2}$ on $Q$ due to charge $q$ at $B =\frac{3}{4 \pi \varepsilon_{0}} \frac{ Q q}{l^{2}}$ along $BO$
Force $F_{3}$ on $Q$ due to charge $q$ at $C=\frac{3}{4 \pi \varepsilon_{0}} \frac{Q q}{l^{2}}$ along $CO$
The resultant of forces $F _{2}$ and $F _{3}$ is $\frac{3}{4 \pi \varepsilon_{0}} \frac{Q q}{l^{2}}$ along $OA$. by the parallelogram law. Therefore, the total force on $g=\frac{3}{4 \pi \varepsilon_{0}} \frac{Q q}{l^{2}}(\hat{ r }-\hat{ r })$
$=0,$ where $\hat{ r }$ is the unit vector along $OA$.
It is clear also by symmetry that the three forces will sum to zero. Suppose that the resultant force was non-zero but in some direction. Consider what would happen if the system was rotated through $60^{\circ}$ about $O$.
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Force of attraction between two point charges $Q$ and $-Q$ separated by $d\,$ metre is ${F_e}$. When these charges are placed on two identical spheres of radius $R = 0.3\,d$ whose centres are $d\,$ metre apart, the force of attraction between them is
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- [AIIMS 1995]
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 = $1.6 \times {10^{ - 27}}\,kg,$ $\,G = 6.7 \times {10^{ - 11}}\,N{m^2}/k{g^2})$
Coulomb's law for electrostatic force between two point charges and Newton's law for gravitational force between two stationary point masses, both have inverse-square dependence on the distance between the charges and masses respectively.
$(a)$ Compare the strength of these forces by determining the ratio of their magnitudes $(i)$ for an electron and a proton and $(ii)$ for two protons.
$(b)$ Estimate the accelerations of electron and proton due to the electrical force of their mutual attraction when they are $1 \mathring A \left( { = {{10}^{ - 10}}m} \right)$ apart? $\left(m_{p}=1.67 \times 10^{-27} \,kg , m_{e}=9.11 \times 10^{-31}\, kg \right)$
Coulomb's law for electrostatic force between two point charges and Newton's law for gravitational force between two stationary point masses, both have inverse-square dependence on the distance between the charges and masses respectively.
$(a)$ Compare the strength of these forces by determining the ratio of their magnitudes $(i)$ for an electron and a proton and $(ii)$ for two protons.
$(b)$ Estimate the accelerations of electron and proton due to the electrical force of their mutual attraction when they are $1 \mathring A \left( { = {{10}^{ - 10}}m} \right)$ apart? $\left(m_{p}=1.67 \times 10^{-27} \,kg , m_{e}=9.11 \times 10^{-31}\, kg \right)$
Two free point charges $+q$ and $+4q$ are a distance $R$ apart. $A$ third charge is so placed that the entire system is in equilibrium. Then the third charge is :-
Two free point charges $+q$ and $+4q$ are a distance $R$ apart. $A$ third charge is so placed that the entire system is in equilibrium. Then the third charge is :-