A 2.2 C charge is located on the x-axis at x = -1.5 m. A 5.4 C charge is located on the x-axis at x = 2.0m. A 3.5 C 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 C charge, we can use Coulomb's Law. Coulomb's Law states that the force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between their centers. Mathematically, it can be written as:
F = (k * q1 * q2) / r^2
where F is the force, k is Coulomb's constant (9 × 10^9 Nm^2/C^2), q1 and q2 are the charges, and r is the distance between the charges.
In this scenario, we have three charges: a +2.2 C charge at x = -1.5 m, a +5.4 C charge at x = 2.0 m, and a +3.5 C charge at the origin (x = 0).
To find the net force on the +3.5 C charge, we need to calculate the forces exerted on it by the +2.2 C and +5.4 C charges, and then add them together as vectors.
Let's start with the force exerted on the +3.5 C charge by the +2.2 C charge. The distance between them is (-1.5 m - 0 m) = -1.5 m (negative because the +2.2 C charge is to the left of the origin). Plugging these values into Coulomb's Law, we get:
F1 = (k * q1 * q2) / r^2
= (9 × 10^9 Nm^2/C^2) * (2.2 C) * (3.5 C) / (-1.5 m)^2
Similarly, let's calculate the force exerted on the +3.5 C charge by the +5.4 C charge. The distance between them is (2.0 m - 0 m) = 2.0 m (positive because the +5.4 C charge is to the right of the origin). Using Coulomb's Law, we have:
F2 = (k * q1 * q2) / r^2
= (9 × 10^9 Nm^2/C^2) * (5.4 C) * (3.5 C) / (2.0 m)^2
Now, we add the forces together as vectors:
F_net = F1 + F2
Here, you can substitute the calculated values for F1 and F2 to find the net force.