A neutral point is a point where resultant electrical field is zero. It is obtained where two electrical field are equal and opposite. Thus neutral points can be obtained only at those points where the resultant field is subtractive.

At an internal point along the line joining two like charges (Due to a system of two like point charge):

Suppose two like charges. Q₁ and Q₂ are separated by a distance x from each other along a line as shown in following figure.

If N is the neutral position at a distance x₁ from Q₁ and at a distance x₂ (= x - x₁) from Q₂ then:

At N | E.F. due to Q₁ | = | E.F. due to Q₂ |

i.e.,   

Short trick:  

At an external point long the line joining two like charges (Due to a system of two unlike point charge):

Consider two unlike charge Q₁ and Q₂ separated by a distance x from each other.

Here neutral position relays outside the line joining two unlike charges and also it lies nearer to charge which is smaller in magnitude.

If | Q₁ | < | Q₂ | then neutral point will be obtained on the side of Q₁, suppose it is at a distance l from Q₁

Hence at neutral point ;

Short trick:      

Zero potential:

If both charges are like then resultant potential is not zero at any finite point because potentials due to like charges will have same sign and can therefore never add up to zero such a point can be therefore obtained only at infinity.

If the particles are unequal and unlike then all such points where resultant potential is zero on a closed curve, but we are interested only in those points where potential is zero along the line joining the two charges.

Two such points exist, one lies inside and one lies outside the charges on the line joining the charged particle. Both the above position lie nearer the smaller charge, as potential created by the charge larger in magnitude will become equal to the potential crated by smaller charge at the desired point at larger distance from it.

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