___A
__/__\
B/____\C
radius (each side of this equilateral triangle) 0.5 m
Three point charges are located at the corners of an equilateral triangle as in the figure below. Find the magnitude and direction (counterclockwise from the +x-axis of the net electric force on the 0.70 µC charge. (Let A = 0.70 µC, B = 6.90 µC, and C = −4.10 µC.)
887.083
To find the net electric force on the 0.70 µC charge, we can use Coulomb's law. Coulomb's law states that the magnitude of the electric force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
To find the magnitude of the net electric force, we need to calculate the individual forces between the 0.70 µC charge and each of the other charges (B and C), and then add them up.
The formula for the magnitude of the electric force is:
F = k * |q1 * q2| / r^2
Where:
- F is the magnitude of the electric force
- k is the electrostatic constant (9 * 10^9 N m^2/C^2)
- q1 and q2 are the charges on the objects
- r is the distance between the charges
Let's calculate the force between charges A and B first:
F_AB = k * |A * B| / r^2
Using the given values:
- A = 0.70 µC
- B = 6.90 µC
- r = 0.5 m
Plugging these values into the formula:
F_AB = (9 * 10^9 N m^2/C^2) * |(0.70 * 10^-6 C) * (6.90 * 10^-6 C)| / (0.5 m)^2
Calculate this expression to find the force between charges A and B.
Similarly, calculate the force between charges A and C:
F_AC = k * |A * C| / r^2
Using the given values:
- A = 0.70 µC
- C = -4.10 µC (note the negative sign indicating opposite charge)
- r = 0.5 m
Plugging these values into the formula:
F_AC = (9 * 10^9 N m^2/C^2) * |(0.70 * 10^-6 C) * (-4.10 * 10^-6 C)| / (0.5 m)^2
Calculate this expression to find the force between charges A and C.
Now that you have the forces F_AB and F_AC, you can find the net force on charge A by adding them together. Remember to consider the directions and signs of the forces.
To find the direction of the net electric force, you can use the concept of vector addition. The direction will be counterclockwise from the +x-axis. Using trigonometry, you can calculate the angle between the x-axis and the net force vector.
Note: Ensure that all the units are consistent throughout the calculations.