Three point charges are on the x axis: −6 µC at −3 m, 7 µC at the origin, and −5 µC at 3 m.
Find the force on the first charge.
The value of the Coulomb constant is
8.98755 × 10^9 N · m^2/C^2.
k=8.98755 × 10^9 =9•10 ⁹N • m^2/C^2.
q1=−6 µC, q2 =7 µC, q3 =-5 µC
F12=k•q1•q2/r1²=9•10⁹•6•10⁻⁶•7•10⁻⁶/9 =….
(to the right)
F13=k•q1•q3/r2²=9•10⁹•6•10⁻⁶•5•10⁻⁶/36 =…
(to the left)
F=F12-F13=…
(to the right)
To find the force on the first charge, we need to calculate the electrostatic force between the first charge and the other two charges.
The electrostatic force between two point charges can be calculated using Coulomb's law:
F = k * (|q1| * |q2|) / r^2
where F is the force between the charges, k is the Coulomb constant, q1 and q2 are the magnitudes of the charges, and r is the distance between the charges.
In this case, the first charge is -6 µC at -3 m. Let's call this charge q1. The second charge is 7 µC at the origin, and the third charge is -5 µC at 3 m. Let's call these charges q2 and q3, respectively.
We can calculate the force between q1 and q2, as well as the force between q1 and q3, and then add them together to find the total force on q1.
Step 1: Calculate the force between q1 and q2
q1 = -6 µC
q2 = 7 µC
r12 = distance between q1 and q2 = 3 m
F12 = k * (|q1| * |q2|) / r12^2
= (8.98755 × 10^9 N · m^2/C^2) * (6 × 10^-6 C) * (7 × 10^-6 C) / (3 m)^2
Step 2: Calculate the force between q1 and q3
q1 = -6 µC
q3 = -5 µC
r13 = distance between q1 and q3 = 6 m
F13 = k * (|q1| * |q3|) / r13^2
= (8.98755 × 10^9 N · m^2/C^2) * (6 × 10^-6 C) * (5 × 10^-6 C) / (6 m)^2
Step 3: Add the two forces together to find the total force on q1
Ftotal = F12 + F13
Now, let's plug in the values and calculate:
F12 = (8.98755 × 10^9 N · m^2/C^2) * (6 × 10^-6 C) * (7 × 10^-6 C) / (3 m)^2
≈ 0.226 N
F13 = (8.98755 × 10^9 N · m^2/C^2) * (6 × 10^-6 C) * (5 × 10^-6 C) / (6 m)^2
≈ 0.062 N
Ftotal = 0.226 N + 0.062 N
≈ 0.288 N
Therefore, the force on the first charge is approximately 0.288 N.
To find the force on the first charge, we need to calculate the individual forces between the first charge and the other two charges.
The formula to calculate the force between two point charges is given by Coulomb's Law:
F = k * |q1 * q2| / r^2
Where:
F is the force between the two charges,
k is the Coulomb constant,
q1 and q2 are the magnitudes of the charges, and
r is the distance between the charges.
Let's calculate the forces between the first charge and the other two charges step-by-step:
1. First, let's calculate the force between the first charge and the second charge.
Given:
q1 = -6 µC (charge of the first charge)
q2 = 7 µC (charge of the second charge)
r = 3 m (distance between the two charges)
Using Coulomb's Law:
Force between the first charge and the second charge (F1-2) = k * |q1 * q2| / r^2
Plugging in the values:
F1-2 = (8.98755 × 10^9 N · m^2/C^2) * |-6 µC * 7 µC| / (3 m)^2
Calculating:
F1-2 = (8.98755 × 10^9 N · m^2/C^2) * (6 × 10^-6 C)(7 × 10^-6 C) / (3)^2
F1-2 = (8.98755 × 10^9 N · m^2/C^2) * (42 × 10^-12 C^2) / 9
F1-2 = (8.98755 × 10^9 N · m^2/C^2) * 4.6667 × 10^-12 C^2
F1-2 ≈ 4.0439 N (rounded to four decimal places)
2. Next, let's calculate the force between the first charge and the third charge.
Given:
q1 = -6 µC (charge of the first charge)
q3 = -5 µC (charge of the third charge)
r = 3 m (distance between the two charges)
Using Coulomb's Law:
Force between the first charge and the third charge (F1-3) = k * |q1 * q3| / r^2
Plugging in the values:
F1-3 = (8.98755 × 10^9 N · m^2/C^2) * |-6 µC * (-5 µC)| / (3 m)^2
Calculating:
F1-3 = (8.98755 × 10^9 N · m^2/C^2) * (30 × 10^-12 C^2) / 9
F1-3 = (8.98755 × 10^9 N · m^2/C^2) * 3.3333 × 10^-12 C^2
F1-3 ≈ 2.9964 N (rounded to four decimal places)
3. Finally, let's find the net force on the first charge by summing up the forces:
Net force on the first charge = F1-2 + F1-3
Net force on the first charge ≈ 4.0439 N + 2.9964 N
Net force on the first charge ≈ 7.0403 N (rounded to four decimal places)
Therefore, the force on the first charge is approximately 7.0403 Newtons.