Two identical metal balls of radius $r$ are at a distance $a (a >> r)$ from each other and are charged, one with potential $V_1$ and other with potential $V_2$. The charges $q_1$ and $q_2$ on these balls in $CGS$ esu are
Two identical metal balls of radius $r$ are at a distance $a (a >> r)$ from each other and are charged, one with potential $V_1$ and other with potential $V_2$. The charges $q_1$ and $q_2$ on these balls in $CGS$ esu are
- A
${q_1} = \frac{{r{V_1} + a{V_1}}}{{{r^2} + {a^2}}},{q_2} = \frac{{r{V_1} + a{V_2}}}{{{r^2} + {a^2}}}$
- B
${q_1} = \frac{1}{k}\left( {\frac{{r{V_2} - a{V_1}}}{{{r^2} - {a^2}}}} \right)ra,{q_2} = \frac{1}{k}\left( {\frac{{r{V_1} - a{V_2}}}{{{r^2} - {a^2}}}} \right)ra$
- C
${q_1} = \frac{{a{V_2}}}{{k\left( {{r^2} - {a^2}} \right)}},{q_2} = \frac{{r{V_1}}}{{k\left( {{r^2} - {a^2}} \right)}}$
- D
${q_1} = \frac{{r{V_1}}}{{k\left( {{r^2} - {a^2}} \right)}},{q_2} = \frac{{r{V_2}}}{{\left( {{r^2} - {a^2}} \right)k}}$
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- [IIT 1981]
Six charges are placed around a regular hexagon of side length a as shown in the figure. Five of them have charge $q$, and the remaining one has charge $x$. The perpendicular from each charge to the nearest hexagon side passes through the center $O$ of the hexagon and is bisected by the side.
Which of the following statement($s$) is(are) correct in SI units?
$(A)$ When $x=q$, the magnitude of the electric field at $O$ is zero.
$(B)$ When $x=-q$, the magnitude of the electric field at $O$ is $\frac{q}{6 \pi \epsilon_0 a^2}$.
$(C)$ When $x=2 q$, the potential at $O$ is $\frac{7 q}{4 \sqrt{3} \pi \epsilon_0 a}$.
$(D)$ When $x=-3 q$, the potential at $O$ is $\frac{3 q}{4 \sqrt{3} \pi \epsilon_0 a}$.
Six charges are placed around a regular hexagon of side length a as shown in the figure. Five of them have charge $q$, and the remaining one has charge $x$. The perpendicular from each charge to the nearest hexagon side passes through the center $O$ of the hexagon and is bisected by the side.
Which of the following statement($s$) is(are) correct in SI units?
$(A)$ When $x=q$, the magnitude of the electric field at $O$ is zero.
$(B)$ When $x=-q$, the magnitude of the electric field at $O$ is $\frac{q}{6 \pi \epsilon_0 a^2}$.
$(C)$ When $x=2 q$, the potential at $O$ is $\frac{7 q}{4 \sqrt{3} \pi \epsilon_0 a}$.
$(D)$ When $x=-3 q$, the potential at $O$ is $\frac{3 q}{4 \sqrt{3} \pi \epsilon_0 a}$.
- [IIT 2022]