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A point particle of charge Q is located at P along the axis of an electric dipole 1 at a distance r as shown in the figure. The point P is also on the equatorial plane of a second electric dipole 2 at a distance r . The dipoles are made of opposite charge q separated by a distance 2 a . For the charge particle at P not to experience any net force, which of the following correctly describes the situation?

Options

  1. Aa r 10
  2. Ba r 20
  3. Ca r 0.5
  4. Da r 3

Correct answer

D. a r 3

Step-by-step solution

aligned & 1 (r-a)^2 - 1 (r+a)^2 = 2 a (a^2+r^2 )^ 3 / 2 & 4 a r (r^2-a^2 )^2 = 2 a (a^2+r^2 )^ 3 / 2 & (r^2-a^2 )^2=2 r (a^2+r^2 )^ 3 / 2 & (1- a^2 r^2 )^2=2 (1+ a^2 r^2 )^ 3 / 2 & (1-x^2 )^2=2 (1+x^2 )^ 3 / 2 (x= a r ) & (1-x^2 )^2 (1+x^2 )^ 3 / 2 =2 aligned Now for X =3 We get 64 10 10 2 a r 3 [But for a > r point charge will between the dipole where E 0 ]

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