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Ques. 1JEE Main 2025, 23 January (Morning Shift)
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 2a. For the charge particle at P not to experience any net force, which of the following correctly describes the situation? [figure]
- ar 0.5
- ar 3
- ar 10
- ar 20
Answer
(2) ar 3
Solution
Net force on Q is zero when E1=E2 at P (they act in opposite directions).
[figure]
Axis of dipole 1: E1= 4kq ra(r2-a2)2; equator of dipole 2: E2= 2kq a(r2+a2)3/2
E1=E2 2(1+x2)3/2=(1-x2)2, with x= ar
x=3: LHS =63.2 RHS =64; the other values are far off
ar 3
Answer: (2)