A charge q1 = 5 µC is at the origin, and a charge q2 = 4 µC is on the x axis at x = 6 m. Find the force on charge q2 . The Colulomb constant is 8.98755 × 10^9 N·m^2/C^2.
Answer in units of N.
b. Find the force on q1. Answer in units of N
c. If an object contains the same number of electrons as protons, it is said to be
1. negatively charged.
2. neutral.
3. positively charged.
4. energized.
To find the force on charge q2 due to charge q1, we can use Coulomb's Law.
Coulomb's Law states that the force between two point charges is directly proportional to the product of their magnitudes 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 = Force between the charges
k = Coulomb's constant (8.98755 × 10^9 N·m^2/C^2)
q1, q2 = Magnitudes of the charges
r = Distance between the charges
In this case, q1 = 5 µC = 5 × 10^-6 C
and q2 = 4 µC = 4 × 10^-6 C
The distance r between the charges is given as 6 m.
Substituting these values into the formula, we have:
F = (8.98755 × 10^9 N·m^2/C^2) * ((5 × 10^-6 C) * (4 × 10^-6 C)) / (6 m)^2
Simplifying this expression, we have:
F = (8.98755 × 10^9 N·m^2/C^2) * (20 × 10^-12 C^2) / (36 m^2)
F = (8.98755 × 10^9 N·m^2/C^2) * (20 × 10^-12 C^2) / (36 × 1) [since m^2 = 1]
F = (8.98755 × 10^9 N·m^2/C^2) * (20 × 10^-12 C^2) / 36
Calculating this expression, we get:
F ≈ 1.249 N
Therefore, the force on charge q2 is approximately 1.249 N.
To find the force on charge q2, we can use Coulomb's law, which states that the force between two charges is directly proportional to the product of the 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, k is the Coulomb constant (8.98755 × 10^9 N·m^2/C^2), q1 and q2 are the charges, and r is the distance between the charges.
Let's plug in the given values into the formula:
q1 = 5 µC = 5 × 10^-6 C
q2 = 4 µC = 4 × 10^-6 C
We know that q1 is at the origin, so its position is (0, 0).
q2 is on the x-axis at x = 6 m. Since q1 is at the origin, the distance between q1 and q2 is simply 6 m.
Substituting the values into the formula, we have:
F = (8.98755 × 10^9 N·m^2/C^2 * |5 × 10^-6 C * 4 × 10^-6 C|) / (6 m)^2
Now, let's calculate the force:
F = (8.98755 × 10^9 N·m^2/C^2 * 20 × 10^-12 C^2) / 36 m^2
F = (8.98755 × 10^9 N·m^2/C^2 * 20 × 10^-12 C^2) / (36 m^2)
F = (179751 × 10^-3 N*m^2)/36 m^2
F = 4993.0833 N
Therefore, the force on charge q2 is approximately 4993.0833 N.