Three point charges, +6.5 μC, +1.8 μC, and −3.4 μC, lie along the x-axis at 0 cm, 1.7 cm, and 5.4 cm, respectively.
What is the force exerted on q1 by the other two charges? (To the right is positive.) The Coulomb constant is 8.99 × 109 N · m2/C2.
Answer in units of N.
F = kq1q2/r^2
Do for both and add noting they will have opposite direction because of the sign on the charges.
To find the force exerted on q1 by the other two charges, we need to use Coulomb's Law, which states that the force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
The formula for Coulomb's Law is:
F = k * ( |q1 * q2| / r^2)
Where:
F is the force between the charges,
k is the Coulomb constant (k = 8.99 × 10^9 N · m^2/C^2),
q1 and q2 are the charges, and
r is the distance between the charges.
In this case, we have three charges. Let's call them q1, q2, and q3. We want to find the force on q1, so we need to consider the charges q2 and q3.
Let's calculate the force exerted on q1 by q2 first:
F21 = k * ( |q1 * q2| / r21^2)
q1 = +6.5 μC,
q2 = +1.8 μC,
r21 = 1.7 cm (0.017 m) [The distance between q2 and q1]
Substituting the given values:
F21 = (8.99 × 10^9 N · m^2/C^2) * ( |(6.5 μC) * (1.8 μC)| / (0.017 m)^2)
Now, let's calculate the force exerted on q1 by q3:
F31 = k * ( |q1 * q3| / r31^2)
q1 = +6.5 μC,
q3 = -3.4 μC,
r31 = 5.4 cm (0.054 m) [The distance between q3 and q1]
Substituting the given values:
F31 = (8.99 × 10^9 N · m^2/C^2) * ( |(6.5 μC) * (-3.4 μC)| / (0.054 m)^2)
To find the total force on q1, we need to add F21 and F31:
Total force on q1 = F21 + F31
Substituting the values we calculated before, we can find the total force on q1.
Note: Make sure to convert the charges to Coulombs and the distances to meters before substituting them into the formula.