Consider three charged particles placed along the x-axis. The particle with q1 = 9.27 nC is at x = 7.66 m and q2 = 4.82 nC is at x = 2.64 m. Where must a positive charge, q3, be placed such that the resultant force on it is zero?

I know F3= F13+ F23
(net force on charge q3 = force 1 on 3 + force 2 on 3)
and that you determine F13 and F23 using columbs law:
ke(q1*q2)/r^2
So you would, Write an expression for the force that each of the other two charges exert on q3 and then set the value of the total force equal to zero.
but I don't know what values of r I would use for each expression.

To determine the values of 'r' for each expression, we need to consider the distance between each charge and the location of the unknown charge q3. Let's assume that q3 is placed at a distance 'x' on the x-axis.

The distance 'r' between q1 and q3 would be the difference in their x-coordinates: r13 = |x - 7.66 m|

Similarly, the distance 'r' between q2 and q3 would be: r23 = |x - 2.64 m|

Now, we can express the forces between q1 and q3, and q2 and q3 using Coulomb's Law:

F13 = k * (q1 * q3) / (r13)^2
F23 = k * (q2 * q3) / (r23)^2

Here, k represents Coulomb's constant (k = 8.99 x 10^9 Nm^2/C^2).

To find the position at which the resultant force on q3 is zero, we set the total force (F3) equal to zero:

F3 = F13 + F23 = 0

Now, substitute the expressions of F13 and F23:

k * (q1 * q3) / (r13)^2 + k * (q2 * q3) / (r23)^2 = 0

Plugging in the given values of q1 and q2, and substituting the expressions for r13 and r23, we get:

(8.99 x 10^9 Nm^2/C^2) * (9.27 nC * q3) / (|x - 7.66 m|)^2 + (8.99 x 10^9 Nm^2/C^2) * (4.82 nC * q3) / (|x - 2.64 m|)^2 = 0

Now, you can solve this equation for the unknown charge position 'x' by rearranging the terms and solving the resulting equation.

Sorry no help is online right now, and i cant help you on this one. Sorry!

The resultant force cannot be zero since all are positive charges