A charge of -3.10 nC and a charge of -6.65 nC are separated by a distance of 80.0 cm. Find the position at which a third charge of +7.10 nC can be placed so that the net electrostatic force on it is zero.
To find the position at which the net electrostatic force on the third charge is zero, we can use Coulomb's Law, which states that the electrostatic force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
Coulomb's Law:
F = k * (|q1| * |q2|) / r^2
Where:
F is the electrostatic force
k is the electrostatic constant (k = 8.99 × 10^9 Nm^2/C^2)
q1 and q2 are the magnitudes of the charges
r is the distance between the charges
Let's assume the third charge is located at a distance x from the -3.10 nC charge.
Now, we need to set up an equation with the electrostatic forces between the charges to find the position where the net force is zero.
The electrostatic force between the +7.10 nC charge and the -3.10 nC charge is given by:
F1 = k * (|q1| * |q3|) / (0.8 - x)^2
The electrostatic force between the +7.10 nC charge and the -6.65 nC charge is given by:
F2 = k * (|q2| * |q3|) / (x)^2
Since we want the net force to be zero, we can write the equation as:
F1 + F2 = 0
Substituting the values, we get:
k * (|q1| * |q3|) / (0.8 - x)^2 + k * (|q2| * |q3|) / (x)^2 = 0
Solving this equation will give us the position x at which the net electrostatic force on the third charge is zero.
Note: Since the charges are in nanoCoulombs, we need to convert them to Coulombs before substituting the values into the equation.