A system of three charges are placed as shown in the figure.

If  $D > > d,$ the potential energy of the system is best given $b$

JEE MAIN 2019, Diffcult
Download our app for free and get startedPlay store
$U_{total}$ $=$ $U_{self\,of\, dipole} + U_{interaction}$

$=-\frac{k q^{2}}{d}-\left(\frac{k Q}{D^{2}}\right) q d$

$=-k\left[\frac{q^{2}}{d}+\frac{q Q d}{D^{2}}\right]$

art

Download our app
and get started for free

Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*

Similar Questions

  • 1
    Two equal capacitors are first connected in series and then in parallel. The ratio of the equivalent capacities in the two cases will be
    View Solution
  • 2
    A molecule of a substance has permanent dipole moment $p$. A mole of this substance is polarised by applying a strong electrostatic field $E$. The direction of the field is suddenly changed by an angle of $60^{\circ} .$ If $N$ is the Avogadro's number the amount of work done by the field is
    View Solution
  • 3
    In the transient current circuit shown, the time constant is
    View Solution
  • 4
    Condenser $A$ has a capacity of $15\,\mu F$ when it is filled with a medium of dielectric constant $15$. Another condenser $B$ has a capacity of $1\,\mu F$ with air between the plates. Both are charged separately by a battery of $100\;V$. After charging, both are connected in parallel without the battery and the dielectric medium being removed. The common potential now is.....$V$
    View Solution
  • 5
    What is the effective capacitance between $A$ and $B$ in the following figure........$\mu \,F$
    View Solution
  • 6
    Two metallic spheres of radii $1\,\, cm$ and $3\,\, cm$ are given, charges of $-1$$ \times {10^{ - 2}}$ $C$ and $5$$ \times {10^{ - 2}}\,C$ respectively. If these are connected by a conducting wire, the final charge on the bigger sphere is
    View Solution
  • 7
    A proton has a mass $1.67 \times 10^{-27} \,kg$ and charge $+1.6 \times 10^{-19} \,C$. If the proton is accelerated through a potential difference of million volts, then the kinetic energy is ......... $J$
    View Solution
  • 8
    The distance between charges $+\mathrm{q}$ and $-\mathrm{q}$ is $2 l$ and between $+2 \mathrm{q}$ and $-2 \mathrm{q}$ is $4 l$. The electrostatic potential at point $P$ at a distance $r$ from centre $O$ is $-\alpha\left[\frac{q l}{r^2}\right] \times 10^9 \mathrm{~V}$, where the value of $\alpha$ is____. (Use $\left.\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \mathrm{Nm}^2 \mathrm{C}^{-2}\right)$
    View Solution
  • 9
    Consider the arrangement shown in figure. The total energy stored is $U_1$ when key is closed. Now the key $K$ is made off (opened) and two dielectric slabs of relative permittivity ${ \in _r}$ are introduced between the plates of the two capacitors. The slab tightly fit in between the plates. The total energy stored is now $U_2$. Then the ratio of $U_1/U_2$ is
    View Solution
  • 10
    In the following diagram, the charge and potential difference across $8\, \mu F$ capacitance will be respectively
    View Solution