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

Question

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?

TestHub · Accepted Answer

​ ⇒ ( r − a ) 2 1 ​ − ( r + a ) 2 1 ​ = ( a 2 + r 2 ) 3/2 2 a ​ ( r 2 − a 2 ) 2 4 a r ​ = ( a 2 + r 2 ) 3/2 2 a ​ ( r 2 − a 2 ) 2 = 2 r ( a 2 + r 2 ) 3/2 ( 1 − r 2 a 2 ​ ) 2 = 2 ( 1 + r 2 a 2 ​ ) 3/2 ( 1 − x 2 ) 2 = 2 ( 1 + x 2 ) 3/2 ( x = r a ​ ) ( 1 + x 2 ) 3/2 ( 1 − x 2 ) 2 ​ = 2 ​ Now for X = 3 We get 10 10 ​ 64 ​ ≈ 2 ⇒ r a ​ ≈ 3 [But for a > r point charge will between the dipole where E  = 0 ]

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