A 2.2 uC charge is located on the x-axis at x = -1.5 m. A 5.4 uC charge is located on the x-axis at x = 2.0m. A 3.5 uC charge is at the origin. Find the net force acting on the 3.5 C charge.
To find the net force acting on the 3.5 uC charge, we need to calculate the individual forces between the 3.5 uC charge and the other charges, and then add them up vectorially.
The force between two charges can be calculated using Coulomb's Law:
F = (k * |q1 * q2|) / r^2
Where:
- F is the magnitude of the force between the charges,
- k is the Coulomb's constant (k = 8.99 x 10^9 N m^2 / C^2),
- q1 and q2 are the magnitudes of the charges,
- r is the distance between the charges.
Let's calculate the magnitude and direction of the force between the 3.5 uC charge and the 2.2 uC charge. The distance between them is the difference between their x-positions:
r1 = |2.0 m - 0 m| = 2.0 m
Using Coulomb's Law:
F1 = (k * |q1 * q2|) / r1^2
= (8.99 x 10^9 N m^2 / C^2) * (3.5 x 10^-6 C) * (2.2 x 10^-6 C) / (2.0 m)^2
Calculating this, we get F1 = 3.69 x 10^-2 N. This force is attractive because the charges have opposite signs and will attract each other.
Next, let's calculate the magnitude and direction of the force between the 3.5 uC charge and the 5.4 uC charge. The distance between them is the sum of their x-positions (since they are on the same side of the origin):
r2 = |2.0 m - 0 m + 1.5 m| = 3.5 m
Using Coulomb's Law:
F2 = (k * |q1 * q2|) / r2^2
= (8.99 x 10^9 N m^2 / C^2) * (3.5 x 10^-6 C) * (5.4 x 10^-6 C) / (3.5 m)^2
Calculating this, we get F2 = 3.08 x 10^-2 N. This force is repulsive because the charges have the same sign and will repel each other.
Now, we can find the net force acting on the 3.5 uC charge by adding up the forces vectorially:
Net force = F1 - F2
Substituting the values we calculated, we get:
Net force = (3.69 x 10^-2 N) - (3.08 x 10^-2 N)
= 6.1 x 10^-3 N
Therefore, the net force acting on the 3.5 uC charge is 6.1 x 10^-3 N in the direction given by the vector subtraction.