Two point charges of `+1muC and +4muC` are kept 30 cm apart. How far from the `+1muC` charge on the line joining the two charges, will the net electric field be zero?

Explanation

Let charges of `q_(1)=1muC and q_(2)=+4muC` be kept fixed at point A and B respectively situated at a distance 30 cm apart. Let net electric field be zero at a point O situated at a distance x cm from charge A as shown in figure. Then, at point O
`vecE_(A)+vecE_(B)=vec0 or |vecE_(A)|= |vecE_(B)| and vecE_(A) and vecE_(B)` must be in mutually opposite directions

`rArr (1)/(4pi in_(0)). (q_(1))/(x^(2))=(1)/(4pi in_(0)). (q_(2))/((30-x)^(2))`
`rArr (1muC)/(x^(2))=(4muC)/((30-x)^(2))rArr x=10cm or 0.1m`