d = distance between the two point charges = 60 cm = 0.60 m
r = distance of the location of point "a" where the electric field is zero from charge [tex]q_{1}[/tex] between the two charges.
[tex]q_{1}[/tex] = magnitude of charge on one charge
[tex]q_{2}[/tex] = magnitude of charge on other charge
[tex]q_{1}[/tex] = 3 [tex]q_{2}[/tex]
[tex]E_{1}[/tex] = Electric field by charge [tex]q_{1}[/tex] at point "a"
[tex]E_{2}[/tex] = Electric field by charge [tex]q_{2}[/tex] at point "a"
Electric field by charge [tex]q_{1}[/tex] at point "a" is given as
[tex]E_{1}[/tex] = k[tex]q_{1}[/tex] /r²
Electric field by charge [tex]q_{2}[/tex] at point "a" is given as
[tex]E_{2}[/tex] = k[tex]q_{2}[/tex] /(d-r)²
For the electric field to be zero at point "a"
[tex]E_{2}[/tex] = [tex]E_{1}[/tex]
k[tex]q_{2}[/tex] /(d-r)² = k[tex]q_{1}[/tex] /r²
[tex]q_{2}[/tex] /(d-r)² = 3[tex]q_{2}[/tex] /r²
1/(0.60 - r)² = 3 /r²
r = 0.38 m
r = 38 cm
