Three point charges are on the x axis: −2 ¦ÌC
at −3 m, 8 ¦ÌC at the origin, and −10 ¦ÌC at
3 m.
Find the force on the first charge.
The value of the Coulomb constant is
8.98755 ¡Á 109 N ¡¤ m2/C2.
Add the Coulomb's-Law forces due to the second and third charges, acting on the first.
To find the force on the first charge, we need to calculate the electric force between the first charge and the other two charges using Coulomb's Law. Coulomb's Law states that the force between two point charges is given by:
F = k * |q1 * q2| / r^2
Where:
- F is the electric force between the charges.
- k is the Coulomb constant, which has a value of 8.98755 × 10^9 N · m^2/C^2.
- q1 and q2 are the magnitudes of the charges.
- r is the distance between the charges.
In this case, the first charge is -2 μC, the second charge is 8 μC, and the third charge is -10 μC.
The distance between the first charge and the second charge is -3 m, and the distance between the first charge and the third charge is 3 m.
Let's calculate the force between the first charge and the second charge first:
F1-2 = k * |q1 * q2| / r^2
F1-2 = (8.98755 × 10^9 N · m^2/C^2) * |-2 μC * 8 μC| / (-3 m)^2
Simplifying the equation:
F1-2 = (8.98755 × 10^9) * (2 μC * 8 μC) / (9 m^2)
Now calculate the force between the first charge and the third charge:
F1-3 = k * |q1 * q2| / r^2
F1-3 = (8.98755 × 10^9 N · m^2/C^2) * |-2 μC * -10 μC| / (3 m)^2
Simplifying the equation:
F1-3 = (8.98755 × 10^9) * (2 μC * 10 μC) / (9 m^2)
Finally, we can find the total force on the first charge by summing up the forces:
Total force on the first charge = F1-2 + F1-3
Plug in the calculated values and perform the addition to find the total force.