A total charge Q is broken in two parts {Q₁} and {Q₂} and they are placed at a distance R from e

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1. Electric Charges and Fields

medium

A total charge $Q$ is broken in two parts ${Q_1}$ and ${Q_2}$ and they are placed at a distance $R$ from each other. The maximum force of repulsion between them will occur, when

${Q_2} = \frac{Q}{R},\;{Q_1} = Q - \frac{Q}{R}$

${Q_2} = \frac{Q}{4},\;{Q_1} = Q - \frac{{2Q}}{3}$

${Q_2} = \frac{Q}{4},\;{Q_1} = \frac{{3Q}}{4}$

${Q_1} = \frac{Q}{2},\;{Q_2} = \frac{Q}{2}$

Solution

(d) ${Q_1} + {Q_2} = Q$ ….. $(i)$ and $F = k\frac{{{Q_1}{Q_2}}}{{{r^2}}}$ …..$(ii)$
From $(i)$ and $(ii)$ $F = \frac{{k{Q_1}(Q – {Q_1})}}{{{r^2}}}$
For $F$ to be maximum $\frac{{dF}}{{d{Q_1}}} = 0$ $==>$ ${Q_1} = {Q_2} = \frac{Q}{2}$

Standard 12

Physics

In the given figure two tiny conducting balls of identical mass $m$ and identical charge $q$ hang from non-conducting threads of equal length $L$. Assume that $\theta$ is so small that $\tan \theta \approx \sin \theta $, then for equilibrium $x$ is equal to

hard

An electron is moving round the nucleus of a hydrogen atom in a circular orbit of radius $r$. The coulomb force $\overrightarrow F $ between the two is (Where $K = \frac{1}{{4\pi {\varepsilon _0}}}$)

medium

(AIPMT-2003)

Dielectric constant of pure water is $81$. Its permittivity will be

easy

Four identical pendulums are made by attaching a small ball of mass $100 \,g$ on a $20 \,cm$ long thread and suspended from the same point. Now, each ball is given charge $Q$, so that balls move away from each other with each thread making an angle of $45^{\circ}$ from the vertical. The value of $Q$ is close to …………..$\mu C$ $\left(\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9\right.$ in $SI$ units $)$

normal

(KVPY-2017)

A negatively charged particle $p$ is placed, initially at rest, in $a$ constant, uniform gravitational field and $a$ constant, uniform electric field as shown in the diagram. What qualitatively, is the shape of the trajectory of the electron?

medium

A total charge $Q$ is broken in two parts ${Q_1}$ and ${Q_2}$ and they are placed at a distance $R$ from each other. The maximum force of repulsion between them will occur, when

Solution

Similar Questions

In the given figure two tiny conducting balls of identical mass $m$ and identical charge $q$ hang from non-conducting threads of equal length $L$. Assume that $\theta$ is so small that $\tan \theta \approx \sin \theta $, then for equilibrium $x$ is equal to

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