A charge $( - q)$ and another charge $( + Q)$ are kept at two points $A$ and $B$ respectively. Keeping the charge $( + Q)$ fixed at $B$, the charge $( - q)$ at $A$ is moved to another point $C$ such that $ABC$ forms an equilateral triangle of side $l$. The net work done in moving the charge $( - q)$ is
A charge $( - q)$ and another charge $( + Q)$ are kept at two points $A$ and $B$ respectively. Keeping the charge $( + Q)$ fixed at $B$, the charge $( - q)$ at $A$ is moved to another point $C$ such that $ABC$ forms an equilateral triangle of side $l$. The net work done in moving the charge $( - q)$ is
- A
$\frac{1}{{4\pi {\varepsilon _0}}}\frac{{Qq}}{l}$
- B
$\frac{1}{{4\pi {\varepsilon _0}}}\frac{{Qq}}{{{l^2}}}$
- C
$\frac{1}{{4\pi {\varepsilon _0}}}Qql$
- D
Zero
Similar Questions
In free space, a particle $A$ of charge $1\,\mu C$ is held fixed at a point $P.$ Another particle $B$ of the same charge and mass $4\,\mu g$ is kept at a distance of $1\,mm$ from $P$. If $B$ is released, then its velocity at a distance of $9\,mm$ from $P$ is [ Take $\frac{1}{{4\pi {\varepsilon _0}}} = 9 \times {10^9}\,N{m^2}{C^{ - 2}}$ ]
In free space, a particle $A$ of charge $1\,\mu C$ is held fixed at a point $P.$ Another particle $B$ of the same charge and mass $4\,\mu g$ is kept at a distance of $1\,mm$ from $P$. If $B$ is released, then its velocity at a distance of $9\,mm$ from $P$ is [ Take $\frac{1}{{4\pi {\varepsilon _0}}} = 9 \times {10^9}\,N{m^2}{C^{ - 2}}$ ]
- [JEE MAIN 2019]
This questions has statement$-1$ and statement$-2$. Of the four choices given after the statements, choose the one that best describe the two statements.
An insulating solid sphere of radius $R$ has a uniformly
positive charge density $\rho$. As a result of this uniform charge distribution there is a finite value of electric potential at the centre of the sphere, at the surface of the sphere and also at a point out side the sphere. The electric potential at infinite is zero.
Statement$ -1$ : When a charge $q$ is take from the centre of the surface of the sphere its potential energy changes by $\frac{{q\rho }}{{3{\varepsilon _0}}}$
Statement$ -2$ : The electric field at a distance $r(r < R)$ from centre of the sphere is $\frac{{\rho r}}{{3{\varepsilon _0}}}$
This questions has statement$-1$ and statement$-2$. Of the four choices given after the statements, choose the one that best describe the two statements.
An insulating solid sphere of radius $R$ has a uniformly
positive charge density $\rho$. As a result of this uniform charge distribution there is a finite value of electric potential at the centre of the sphere, at the surface of the sphere and also at a point out side the sphere. The electric potential at infinite is zero.
Statement$ -1$ : When a charge $q$ is take from the centre of the surface of the sphere its potential energy changes by $\frac{{q\rho }}{{3{\varepsilon _0}}}$
Statement$ -2$ : The electric field at a distance $r(r < R)$ from centre of the sphere is $\frac{{\rho r}}{{3{\varepsilon _0}}}$
- [AIEEE 2012]
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The diagram shows a small bead of mass $m$ carrying charge $q$. The bead can freely move on the smooth fixed ring placed on a smooth horizontal plane. In the same plane a charge $+Q$ has also been fixed as shown. The potential atthe point $P$ due to $+Q$ is $V$. The velocity with which the bead should projected from the point $P$ so that it can complete a circle should be greater than
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- [AIPMT 1999]