Three point charges are placed on the x-axis. A charge of +2.0 μC is placed at the origin, -2.0 μC to the right at x = 50 cm, and +4.0 μC at the 100 cm mark. What are the magnitude and direction of the electrostatic force which acts on the charge at the origin?
Answer
0.072 N right
0.072 N left
0.14 N right
0.14 N left
0.072 right
To find the electrostatic force acting on the charge at the origin, we need to calculate the individual forces between the charge at the origin and the other charges. Then, we can add up the forces to find the net force.
The electrostatic force between two charges can be calculated using Coulomb's law:
F = k * (|q1| * |q2|) / r^2
Here, F is the magnitude of the electrostatic force, k is the electrostatic constant (k = 9 * 10^9 Nm^2/C^2), q1 and q2 are the charges, and r is the distance between the charges.
For the charge at the origin (q1 = +2.0 μC) and the charge at x = 50 cm (q2 = -2.0 μC), the distance between them is 50 cm = 0.5 m.
Calculating the force using Coulomb's law for these two charges:
F1 = (9 * 10^9 Nm^2/C^2) * ((2.0 * 10^(-6) C) * (2.0 * 10^(-6) C)) / (0.5 m)^2
= 72 N
The force between these two charges is 72 N.
For the charge at the origin (q1 = +2.0 μC) and the charge at the 100 cm mark (q2 = +4.0 μC), the distance between them is 100 cm = 1.0 m.
Calculating the force using Coulomb's law for these two charges:
F2 = (9 * 10^9 Nm^2/C^2) * ((2.0 * 10^(-6) C) * (4.0 * 10^(-6) C)) / (1.0 m)^2
= 36 N
The force between these two charges is 36 N.
Since the charge at the origin and the charge at x = 50 cm have opposite signs, their forces are in opposite directions. Therefore, the net force can be found by subtracting F2 from F1:
Net force = F1 - F2
= 72 N - 36 N
= 36 N
The magnitude of the net force is 36 N. Since the force between the charges at the origin and x = 50 cm is greater, the direction of the net force is towards the right.
Therefore, the magnitude and direction of the electrostatic force acting on the charge at the origin is 36 N towards the right.
To find the magnitude and direction of the electrostatic force on the charge at the origin, we can use Coulomb's law. Coulomb's law states that the magnitude of the electrostatic force between two point 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) / r²
Where:
F is the electrostatic force
k is Coulomb's constant (9 × 10^9 N m²/C²)
q₁ and q₂ are the charges
r is the distance between the charges
In this case, the charge at the origin is +2.0 μC (microcoulombs), the charge at x = 50 cm is -2.0 μC, and the charge at the 100 cm mark is +4.0 μC. The distances between the charges are 50 cm and 100 cm.
First, we need to convert the charges from microcoulombs (μC) to coulombs (C):
2.0 μC = 2.0 * 10^-6 C
-2.0 μC = -2.0 * 10^-6 C
4.0 μC = 4.0 * 10^-6 C
Next, convert the distances to meters (m):
50 cm = 0.5 m
100 cm = 1.0 m
Now we can calculate the force:
F₁ = k * (q₁ * q₂) / r₁²
F₂ = k * (q₁ * q₃) / r₂²
F₁ = (9 × 10^9 N m²/C²) * (2.0 * 10^-6 C) * (-2.0 * 10^-6 C) / (0.5 m)²
F₂ = (9 × 10^9 N m²/C²) * (2.0 * 10^-6 C) * (4.0 * 10^-6 C) / (1.0 m)²
Calculating these values: