3 charges are arranged along the x-axis.
q1 = -4.50 nC is located at x = 0.200m
q2 = +2.50 nC is located at x = -0.300m
q3 = is a positive character located at the origin.
What is the value of q3 for the net eletric force on it to be 4*10^-6 N?
I found the charge on q3 to be = 3 nC
Where along the x-axis can q3 be placed so that the net eletric force on it is 0, other than +/- infinity?
This is where I'm stuck.
To find the location along the x-axis where q3 can be placed so that the net electric force on it is zero, we need to use the principle of superposition of electric forces.
First, we need to calculate the electric force between q3 and each of the other charges (q1 and q2).
The electric force between two charges is given by Coulomb's Law:
F = k * (q1 * q2) / r^2
Where:
F is the electric force between the two charges,
k is the electrostatic constant (k = 9.0 x 10^9 N•m^2/C^2),
q1 and q2 are the magnitudes of the charges,
and r is the distance between the charges.
Let's calculate the electric force between q3 and q1:
F1 = k * (q1 * q3) / r1^2
Here, r1 is the distance between q1 and q3, which is 0.200m since q1 is located at x = 0.200m. q1 is -4.50 nC and we are trying to find the value of q3. The force F1 is the sum of the forces acting on q3 due to q1 and q2.
Next, let's calculate the electric force between q3 and q2:
F2 = k * (q2 * q3) / r2^2
Here, r2 is the distance between q2 and q3, which is 0.300m since q2 is located at x = -0.300m. q2 is +2.50 nC and we are trying to find the value of q3. The force F2 is the sum of the forces acting on q3 due to q1 and q2.
Now, to find the net electric force on q3, we add the forces F1 and F2 together:
Fnet = F1 + F2
Given that the net electric force on q3 is 4 * 10^-6 N, we can set up the equation:
4 * 10^-6 N = F1 + F2
Now, we substitute the expressions for F1 and F2 into the equation:
4 * 10^-6 N = (k * (q1 * q3) / r1^2) + (k * (q2 * q3) / r2^2)
Plug in the known values:
4 * 10^-6 N = (9.0 x 10^9 N•m^2/C^2) * (-4.50 nC * q3) / (0.200m)^2 + (9.0 x 10^9 N•m^2/C^2) * (2.50 nC * q3) / (0.300m)^2
Now, solve the equation for q3. This will give you the value of q3 that makes the net electric force on it equal to 4 * 10^-6 N.
Unfortunately, without the values of q1 and q2, it is not possible to determine the exact location along the x-axis where q3 can be placed to make the net electric force zero. To calculate the position, one would need to solve the equation for q3 and then determine the value of x that corresponds to that charge.