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NEET 2017
Exam
NEET
Year
2017
Subject
Physics
Chapter
Electrostatics

NEET 2017 · Physics · Electrostatics

Suppose the charge of a proton and an electron differ slightly. One...

Suppose the charge of a proton and an electron differ slightly. One of them is ee, the other is \left(e + \Deltae\right).Ifthenetelectrostaticforceandgravitationalforcebetweentwohydrogenatomsplacedatadistance. If the net electrostatic force and gravitational force between two hydrogen atoms placed at a distanced(muchgreaterthanatomicsize)apartiszero,then(much greater than atomic size) apart is zero, then\Deltaeisoftheorderof[Givenmassofhydrogenis of the order of [Given mass of hydrogen{m}_{h} = 1.67 \times {10}^{– 27}kg]

Options

  1. A10−20C{10}^{- 20}C
  2. B10−23C{10}^{- 23}C
  3. C10−37C{10}^{- 37}C
  4. D10−47C{10}^{- 47}C

Correct answer

C. 10−37C{10}^{- 37}C

Step-by-step solution

The net electrostatic force and gravitational force will be equal since the net force on the system is zero. Thus, FE=Fg{F}_{E} = {F}_{g}

14πε0Δe2d2=Gm2d2\dfrac{1}{4\pi{ε}_{0}}\dfrac{\Delta{e}^{2}}{{d}^{2}} = \dfrac{G{m}^{2}}{{d}^{2}}

9×109(Δe2)=6.67×10−11×1.67×10−27×1.67×10−279 \times {10}^{9}\left(\Delta{e}^{2}\right) = 6.67 \times {10}^{- 11} \times 1.67 \times {10}^{- 27} \times 1.67 \times {10}^{- 27}

Δe2=6.67×1.67×1.679×10−74\Delta{e}^{2} = \dfrac{6.67 \times 1.67 \times 1.67}{9} \times {10}^{- 74}

\Deltae≈10−37\Deltae \approx {10}^{- 37}
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