A charge of 7.00 10-9 C and a charge of -4.50 10-9 C are separated by a distance of 60.0 cm. Find the position at which a third charge, of 13.0 10-9 C, can be placed so that the net electrostatic force on it is zero.

To find the position at which a third charge can be placed so that the net electrostatic force on it is zero, we can use Coulomb's Law and the principle of vector addition.

1. We know that the electrostatic force between two charged objects is given by Coulomb's Law:
F = k * q1 * q2 / r^2,
where F is the electrostatic force, k is Coulomb's constant (8.99 × 10^9 N m^2/C^2), q1 and q2 are the charges, and r is the distance between the charges.

2. We can calculate the force between the first two charges:
F1 = k * q1 * q2 / r1^2,
where q1 = 7.00 × 10^-9 C, q2 = -4.50 × 10^-9 C, and r1 = 60.0 cm = 0.60 m.

3. We can calculate the force between the third charge and the first charge:
F2 = k * q1 * q3 / r2^2,
where q3 = 13.0 × 10^-9 C and r2 is the distance between the first and third charges.

4. According to the principle of vector addition, the net force on the third charge is zero when the forces are equal in magnitude and opposite in direction:
F2 = F1, but with opposite sign.

5. We can set up a proportion to solve for r2:
k * q1 * q3 / r2^2 = -k * q1 * q2 / r1^2

Simplifying the equation:
q3 / r2^2 = -q2 / r1^2

Rearranging the equation:
r2^2 = -(q2 * r1^2) / q3

Taking the square root of both sides:
r2 = sqrt(-(q2 * r1^2) / q3)

6. Plug in the values:
q2 = -4.50 × 10^-9 C
r1 = 0.60 m
q3 = 13.0 × 10^-9 C

r2 = sqrt(-(q2 * r1^2) / q3)
= sqrt(-( -4.50 × 10^-9 C * (0.60 m)^2) / (13.0 × 10^-9 C))

This gives us the position at which the third charge can be placed to have a net electrostatic force of zero.

It is important to note that the signs in Coulomb's Law indicate the type of charge (positive or negative) and the direction of the force.

To find the position at which the net electrostatic force on the third charge is zero, we need to calculate the distance from the two charges that would result in a net force of zero.

We can use Coulomb's Law to solve this problem. According to Coulomb's Law, the force between two charges is given by:

F = k * |q1 * q2| / r^2

Where:
F is the electrostatic force,
k is the electrostatic constant (k = 8.99 * 10^9 N m^2/C^2),
q1 and q2 are the charges, and
r is the distance between the charges.

Given:
Charge 1 (q1) = 7.00 * 10^-9 C
Charge 2 (q2) = -4.50 * 10^-9 C
Charge 3 (q3) = 13.0 * 10^-9 C
Distance (r) = 60.0 cm = 0.60 m

To make the net force on charge 3 zero, the forces between charge 3 and charges 1 and 2 must be equal in magnitude but opposite in direction. We can set up an equation to solve for the distance (r3) between charge 3 and charges 1 and 2:

F1 = F2

k * |q1 * q3| / r13^2 = k * |q2 * q3| / r23^2

We can rearrange the equation to solve for r13:

r13 = sqrt((|q2 / q1|) * (r23^2))

Plugging in the values:

r13 = sqrt((|-4.50 * 10^-9 C / 7.00 * 10^-9 C|) * (0.60 m)^2)

Simplifying:

r13 = sqrt((4.50 / 7.00) * 0.36) m
= sqrt(0.2314) m
= 0.480 m

Therefore, the position at which the third charge (13.0 * 10^-9 C) can be placed so that the net electrostatic force on it is zero is at a distance of 0.480 m from the charges of 7.00 * 10^-9 C and -4.50 * 10^-9 C.