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Asked by anshuman.anshuman090 | 19 Nov, 2019, 23:43: PM
answered-by-expert Expert Answer
Figure shows the position of dipole and charge as given in question.
 
Let us assume, at point B(x, x+y) electric field due to dipole and point charge vanishes.
 
Electric field at B due to dipole = ( k p 2cosθ ) / (AB)3 ...................(1)
 
where k is 1/(4πεo ) , εo is permitivitty of free space, p is dipole moment and θ is angle made by line AB
with direction of dipole vector
 
Electric field at B due to dipole = [ k p 2 (1/√2)] / 2√2 x3   =  ( k p ) / (2x3 )...................(2)
 
Electric field at B due to point charge = -( k q ) / OB2 = ( k q ) / [ x2 + (x+y)2 ]  ....................(3)
 
( since net field vanishes, point charge is taken as -ve )
 
If net field is zero, magnitude of both the fields should be same. By equating equations (2) and (3), we get
 
  p  / (2x3 )  =  q / [ x2 + (x+y)2 ].................(4)
 
By substituting values for dipole moment p and magnitude of point charge q,
y-coordinate can be expressed in terms of x-coordinate using eqn.(4)
 
Answered by Thiyagarajan K | 21 Nov, 2019, 10:58: AM

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