Given information:
Two fixed point charges, -0.000004C and 0.000001C, are separated from each other by a distance of 1m in air.

Explanation:
To find the point on the line joining the charges where the resultant electric intensity is zero, we can use the principle of superposition of electric fields.

Electric field due to a point charge:
The electric field due to a point charge can be calculated using the formula:
E = k * (q / r^2)
where E is the electric field, k is the electrostatic constant (8.99 x 10^9 Nm^2/C^2), q is the charge, and r is the distance from the charge.

Electric field due to the first charge:
The electric field due to the charge -0.000004C at a distance of 1m can be calculated as:
E1 = (8.99 x 10^9 Nm^2/C^2) * (-0.000004C) / (1m)^2

Electric field due to the second charge:
The electric field due to the charge 0.000001C at a distance of 1m can be calculated as:
E2 = (8.99 x 10^9 Nm^2/C^2) * (0.000001C) / (1m)^2

Resultant electric field:
The resultant electric field at any point on the line joining the charges is the vector sum of the electric fields due to each charge.

Using vector addition:
To find the point where the resultant electric field is zero, we need to find the position on the line joining the charges where the magnitudes of the electric fields due to each charge are equal and opposite.

Mathematical representation:
E1 = -E2

Solving the equation:
Substituting the values of E1 and E2, we can solve the equation to find the position where the resultant electric field is zero.

(8.99 x 10^9 Nm^2/C^2) * (-0.000004C) / (1m)^2 = - (8.99 x 10^9 Nm^2/C^2) * (0.000001C) / (1m)^2

Simplifying the equation will give us the position where the resultant electric field is zero.

Final answer:
The point on the line joining the charges where the resultant electric field is zero can be calculated using the above equation.