Charge q1 = 6 uC is at the origin, charge q2 = 7 uC is at y = 2m, x = 0, charge q3 = 1.5 uC is at y = -1 m, x = 0. What is the force on q2?
Add the forces due to q1 and q3. All charges are located along the x axis.
q1 pushes q2 to the left, and q3 pushes q2 to the right. Therefore you will have to subtract one force from the other to get the difference. Both are forces of repulsion, since all charges are the same.
To compute the force of one particle on another, use Coulomb's law.
F = k q q'/R^2
To find the force on q2, we need to calculate the electric force due to the other charges q1 and q3.
The electric force between two charges can be calculated using Coulomb's Law:
F = k * (|q1*q2| / r^2)
Where:
F is the electric force,
k is the electrostatic constant (k = 8.99 * 10^9 N*m^2/C^2),
|q1*q2| is the absolute value of the product of the charges of q1 and q2,
r is the distance between q1 and q2.
Let's calculate the individual forces due to q1 and q3 and then find the net force on q2.
1. Force due to q1:
The distance between q1 and q2 is the vertical distance, which is 2 meters.
Calculate the electric force between q1 and q2 using Coulomb's Law:
F1 = k * (|q1*q2| / r^2) = (8.99 * 10^9 N*m^2/C^2) * ((6 * 10^-6 C) * (7 * 10^-6 C) / (2 m)^2)
2. Force due to q3:
The distance between q3 and q2 is also the vertical distance, but in the opposite direction, so it will have a negative sign.
Calculate the electric force between q3 and q2 using Coulomb's Law:
F3 = k * (|q3*q2| / r^2) = (8.99 * 10^9 N*m^2/C^2) * ((1.5 * 10^-6 C) * (7 * 10^-6 C) / (3 m)^2)
3. Net force on q2:
The net force on q2 is the vector sum of the forces due to q1 and q3. Since both forces are in the y-direction, we can simply add them together:
Net force on q2 = F1 + F3
Now, plug in the values and calculate the net force on q2.