Question
The electrostatic force of interaction between an uniformly charged rod having total charge $Q$ and length $L$ and a point charge $q$ as shown in figure is
✓
Answer
$\int {{\rm{dF}}} = \int_0^{{\rm{d}} - {\rm{L}}} {\frac{1}{{4\pi { \in _0}}}} \frac{{\left( {\frac{{\rm{Q}}}{{\rm{L}}}{\rm{dx}}} \right){\rm{q}}}}{{{{\rm{x}}^2}}}$
$\Rightarrow \mathrm{F}=\frac{1}{4 \mathrm{n} \in_{0}} \frac{\mathrm{qQ}}{\mathrm{L}}\left|\frac{1}{-\mathrm{x}}\right|_{\mathrm{d}}^{\mathrm{d}+\mathrm{L}}$
$F = \frac{1}{{4\pi { \in _0}}}\frac{{Qq}}{L}\left[ { - \frac{1}{{d + L}} + \frac{1}{d}} \right]$
$ = \frac{1}{{4\pi { \in _0}}}\frac{{qQ}}{L}\left[ {\frac{{ - d + d + L}}{{d(d + L)}}} \right]$
${\rm{F}} = \frac{1}{{4\pi { \in _0}}}\frac{{{\rm{qQ}}}}{{{\rm{d}}({\rm{d}} + {\rm{L}})}}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
A star is going away from the earth. An observer on the earth will see the wavelength of light coming from the star
It takes $2.0$ seconds for a sound wave to travel between two fixed points when the day temperature is ${10^o}C.$ If the temperature rise to ${30^o}C$ the sound wave travels between the same fixed parts in ...... $sec$
→product:-
As the temperature increases, the electrical resistance
$28\,\, gm$ of $N_2$ gas is contained in a flask at a pressure of $10$ atm and at a temperature of $57^o$. It is found that due to leakage in the flask, the pressure is reduced to half and the temperature reduced to $27\,^oC$. The quantity of $N_2$ gas that leaked out is
→The switches in figures $(a)$ and $(b)$ are closed at $t = 0$
→A black hole is an object whose gravitational field is so strong that even light cannot escape from it. To what approximate radius would earth $($ mass $= 5 .98 \times \,10^{24}\, kg)$ have to be compressed to be a black hole?
→In the figure given below, a ray of light travelling in a medium of refractive index $\mu$ passes through two different connected rectangular blocks of refractive indices $\mu_1$ and $\mu_2\left(\mu_2 > \mu_1\right)$ The angle of incidence $\theta_1$ is increased slightly. Then, the angle $\theta_2$ is
→A mixture of two moles of hydrogen and one mole of argon gas is taken in a closed container at room temperature. Consider the following two statements
→$(i)$ The average kinetic energy of each molecule of $H_2$ and $Ar$ are the same.
$(ii)$ The partial pressure due to argon gas is more than that due to hydrogen gas
A coin placed on a rotating table just slips when it is placed at a distance of $1\,cm$ from the center. If the angular velocity of the table in halved, it will just slip when placed at a distance of from the centre $............\,cm$
→