Two point charges \(Q\) each are placed at a distance \(d\) apart. A third point charge \(q\) is placed at a distance \(x\) from mid-point on the perpendicular bisector. The value of \(x\) at which charge \(q\) will experience the maximum \(Coulomb's force\) is ...............

Pick an option to check your answer.

Verified Solution

Answer & Solution

Correct Answer

(D) \(x=\frac{d}{2 \sqrt{2}}\)

Step-by-step Solution

Detailed explanation

\(F =\frac{ KQq }{\left( x ^{2}+\frac{ d ^{2}}{4}\right)}\)

Net force on \(g =2 F \cos \theta\)

\(F _{\text {act }}=\frac{2 KQqx }{\left( x ^{2}+\frac{ d ^{2}}{4}\right)^{3 / 2}}\)

For maximum \(F _{\text {act }}\)

\(\frac{ d F _{\text {net }}}{ dx }=0\)

we get \(x=\frac{d}{2 \sqrt{2}}\)

Same subject

Orange light of wavelength \(6000 \times 10^{-10}\, m\) in illuminates a single slit of width \(0.6 \times 10^{-4}\, m\) The maximum possible number of diffraction minima produced on both sides of the central maximum is\(........\)

JEE Mains 2020 Medium
A reversible engine has an efficiency of \(\frac{1}{4}\). If the temperature of the sink is reduced by \(58^{\circ} {C}\), its efficiency becomes double. Calculate the temperature of the sink. (In \(^{\circ} {C}\))

JEE Mains 2021 Hard
Two wires \(A\) and \(B\) made of different materials of length 6.0 cm and 5.4 cm, respectively and area of cross sections \(3.0 \times 10^{-5} m^2\) and \(4.5 \times 10^{-5} m^2\), respectively are stretched by the same magnitude under a given load. The ratio of the Young's modulus of \(A\) to that of \(B\) is \(x : 3\). The value of x is ___________.

JEE Mains 2026 Easy
A proton and an electron are associated with same de-Broglie wavelength. The ratio of their kinetic energies is _______. (Assume \(\mathrm{h}=6.63 \times 10^{-34} \mathrm{~J} \mathrm{~s}, \mathrm{~m}_{\mathrm{e}}=9.0 \times 10^{-31} \mathrm{~kg}\) and \(\mathrm{m}_{\mathrm{p}}=1836\) times \(\mathrm{m}_{\mathrm{e}}\) )

JEE Mains 2024 Hard
The activity of a radioactive material is \(6.4 \times 10^{-4}\) curie. Its half life is \(5\; days\). The activity will become \(5 \times 10^{-6}\) curie after \(.......day\)

JEE Mains 2022 Medium
If the kinetic energy of a moving body becomes four times its initial kinetic energy, then the percentage change in its momentum will be \(...\%\)

JEE Mains 2021 Medium

Explore more questions on app

From JEE Mains

The ratio of wavelengths of proton and deuteron accelerated by potential \(V_{p}\) and \(V_{d}\) is 1: \(\sqrt{2}\). Then, the ratio of \(V_{p}\) to \(V_{d}\) will be

JEE Mains 2022 Medium
The distance between an object and a screen is \(100\, cm .\) A lens can produce real image of the object on the screen for two different positions between the screen and the object. The distance between these two positions is \(40\, cm .\) If the power of the lens is close to \(\left(\frac{ N }{100}\right) D\) where \(N\) is an integer, the value of \(N\) is.......

JEE Mains 2020 Hard
A particle of mass \(4\, {M}\) at rest disintegrates into two particles of mass \({M}\) and \(3 \,{M}\) respectively having non zero velocities. The ratio of de-Broglie wavelength of particle of mass \(M\) to that of mass \(3\, {M}\) will be :

JEE Mains 2021 Medium

Explore more questions on app