Answer :
If two positive point charges p and q are held a certain distance apart then at the center of the line joining these two point charges , the electric field strength will be zero.
Let the two points say P lies on the origin and the other point Q is “ a ” distance apart from it .
Let the point A at which the electric field is zero lies on the line joining these points , x distance apart from the origin .
According to electrostatics , the electric field strength due to a charge at a point is written as:-
Electric field (E) = Kq/r²
Where K = dielectric constant
q = charge of the point charge
r = distance between the point and the charge
electric field at A due to P
Ep = Kq/x²
Electric field at A due to Q
Eq = Kq/(a-x)²
The net electric field strength at point is 0 as per the question
Ep = Eq
The electric fields cancel outs each other at point A
Kq/x² = Kq/(a-x)²
x² =(a-x)²
x = a – x
2x = a
x = a/2
Hence, point x lies on the midpoint of the line joining the point charges.
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