You place a point charge q = -4.00 nC a distance of 9.00 cm from an infinitely long, thin wire that has linear charge density 3.00×10−9C/m. What is the magnitude of the electric force that the wire exerts on the point charge?
To find the magnitude of the electric force that the wire exerts on the point charge, you can use Coulomb's law. Coulomb's law states that the electric force between two charged objects is given by:
F = k * (|q1| * |q2|) / r^2
Where:
- F is the electric force
- k is the electrostatic constant (k = 8.99 × 10^9 N·m^2/C^2)
- q1 and q2 are the charges of the two objects
- r is the distance between the charges
In this case, the point charge has a magnitude of q = -4.00 nC = -4.00 × 10^-9 C. The linear charge density of the wire is 3.00 × 10^-9 C/m. The distance between them is 9.00 cm = 0.09 m.
Now we can substitute these values into Coulomb's law:
F = (8.99 × 10^9 N·m^2/C^2) * (|-4.00 × 10^-9 C| * |3.00 × 10^-9 C/m|) / (0.09 m)^2
F = (8.99 × 10^9 N·m^2/C^2) * (4.00 × 10^-9 C) * (3.00 × 10^-9 C/m) / (0.09 m)^2
F = 1.196 × 10^-4 N
Therefore, the magnitude of the electric force that the wire exerts on the point charge is approximately 1.196 × 10^-4 N.
To find the magnitude of the electric force that the wire exerts on the point charge, you can use Coulomb's Law. Coulomb's Law states that the magnitude of the electric force between two point charges is given by:
F = k * (|q1| * |q2|) / r^2
Where:
F is the electric force,
k is Coulomb's constant (k = 8.99 × 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 point charge is q = -4.00 nC and the distance from the wire is 9.00 cm. The linear charge density of the wire is given as 3.00×10^-9 C/m. However, since the wire is infinitely long, you only need to consider a small segment of the wire.
To calculate the electric force, you need to determine the charge of the wire segment. The charge q of a wire segment is calculated by multiplying the linear charge density (λ) by its length (L):
q = λ * L
In this case, the length L is the distance between the wire and the point charge, which is 9.00 cm.
So, the charge q of the wire segment is:
q = (3.00×10^-9 C/m) * (9.00 cm) = 2.70 × 10^-10 C.
Now that you have the magnitudes of both charges, q1 = |-4.00 nC| = 4.00 × 10^-9 C and q2 = |2.70 × 10^-10 C|, and the distance r = 9.00 cm, you can substitute these values into Coulomb's Law to find the magnitude of the electric force.