2 point charges -9nC n 16nC are separated by distance 1m find the position along the line joining the charges on which the resultant electric intensity is zero

FORGET k, 10^-6 etc etc which are the same for both

put -9 at x = 0
put + 16 at x = 1

from negative x a + 1 charge
pulled right to x= 0 but pushed left from x = +1
so left of 0, final x is negative

9/x^2 = 16/(1-x)^2

9 (x^2 - 2 x + 1 ) = 16 x^2
9 x^2 - 18 x + 9 = 16 x^2

7 x^2 + 18 x - 9 = 0

x = [ -18 +/-sqrt ( 324 + 252)]/14

use - answer to get spot
[ -18 - 24 ]/14

= -42/14

= -3

3 left of zero where the 9 charge is and 4 left of the 16 charge

===================
CHECK
3 left of -9
force right 9/9 = 1

4 left of + 16
force left 16/16= 1

whew

To find the position along the line joining the charges where the resultant electric intensity is zero, we can use the principle of superposition. The principle states that the electric field due to multiple charges is equal to the vector sum of the individual electric fields produced by each charge.

The formula to calculate the electric field due to a point charge is given by:

E = k * q / r^2

Where:
E is the electric field
k is the electrostatic constant (9 x 10^9 Nm^2/C^2)
q is the charge
r is the distance between the charge and the point where electric field is being calculated

Let's consider two charges, q1 = -9nC and q2 = 16nC, separated by a distance of 1m. We need to find a point along the line joining these charges where the resultant electric intensity is zero.

We can calculate the electric fields due to each charge at any arbitrary point and add them up to find the resultant electric field. When the resultant electric field is zero, we have found the position where the electric intensity is zero.

Let's assume we have a point P at a distance 'x' from the charge q1 and distance '1-x' from the charge q2.

Electric field due to charge q1 at point P:
E1 = k * q1 / (x)^2 (1)

Electric field due to charge q2 at point P:
E2 = k * q2 / (1 - x)^2 (2)

Since the resultant electric intensity is zero, we have E1 + E2 = 0.

Substituting the values of E1 and E2 from equations (1) and (2) into the equation E1 + E2 = 0, we can solve for the value of 'x' to find the position along the line joining the charges where the resultant electric intensity is zero.

k * q1 / (x)^2 + k * q2 / (1 - x)^2 = 0

Solving this equation will give us the position 'x' where the resultant electric intensity is zero.