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QJEEM19Ph354f: JEE Main 2019 Physics - Class 12 JEEM19Ph354f Solution: A system of three charges are placed as shown in the figure :…

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

JEE Main 2019 (Online) 9th April Morning Slot Physics - Electrostatics Question 171 English If D >> d, the potential energy of the system is best given by :

Multiple Choice Options

  • A 14πε0[q2d+qQdD2]{1 \over {4\pi {\varepsilon _0}}}\left[ { {{{q^2}} \over d} + {{qQd} \over {{D^2}}}} \right]
  • B 14πε0[−q2d−qQd2D2]{1 \over {4\pi {\varepsilon _0}}}\left[ { - {{{q^2}} \over d} - {{qQd} \over {2{D^2}}}} \right]
  • C 14πε0[−q2d−qQdD2]{1 \over {4\pi {\varepsilon _0}}}\left[ { - {{{q^2}} \over d} - {{qQd} \over {{D^2}}}} \right]
  • D 14πε0[−q2d+2qQdD2]{1 \over {4\pi {\varepsilon _0}}}\left[ { - {{{q^2}} \over d} + {2{qQd} \over {{D^2}}}} \right]

Step-by-Step Verified Solution

Utotal = Uself of dipole + Uinteraction

= −kq2d−(kQD2)qd- {{k{q^2}} \over d} - \left( {{{kQ} \over {{D^2}}}} \right)qd

=−k[q2d+qQdD2]= - k\left[ {{{{q^2}} \over d} + {{qQd} \over {{D^2}}}} \right]

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