Question

two point charges 1.2 microcoulomb and 0.2 micro coulomb placed at 500 ml apart find the position where net electric field is zero mathematicaly​

Answer 1

As the both the charges have opposite sign that means they are acting in opposite directions, so the zero electric field point is not possible between the two charges , it should occur in any one side. Let us consider the point P where the electric field is zero at a distance x from the negative charge.

So, the diagram is  given below.

Let the point A has the positive charge +16 μC and the point B has the negative charge -9 μC. The distance between the points A and B is 8 cm. Let us consider a point P at a distance x from B. P is the point where the electric field is zero.

The electric field acting on a point due to charge q is,Here k is the constant of proportionality, q is the charge and r is the distance of the point from the charge.

Thus, the electric field acting on point P due to the positive charge at A is,

Similarly, the electric field acting on point P due to the negative charge at B is,

The resultant electric field should be zero at P, so,Taking square root on both the sides,

Thus, the point P should be at a distance of 24 cm from the negative charge and (24+8) cm distance from the positive charge.So the distance between PA is 32 cm and PB is 24 cm.