A dust particle carrying a charge of is 2 mm

to the left of another dust particle carrying a charge of
. Find the magnitude and direction of the elec-
tric force on the first particle.

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To find the magnitude and direction of the electric force on the first particle, we can use Coulomb's Law. Coulomb's Law states that the electric force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

Let's break down the steps to find the electric force:

Step 1: Convert the given distances to meters.
The first particle is 2 mm to the left of the second particle. To use Coulomb's Law, we need to have the distances in meters. Since 1 meter is equal to 1000 mm, we can convert 2 mm to meters by dividing it by 1000.
2 mm ÷ 1000 = 0.002 meters

Step 2: Calculate the electric force using Coulomb's Law.
Coulomb's Law is given by the equation:
F = k * (|q1 * q2|) / r^2

Where:
F is the electric force between the particles,
k is Coulomb's constant (approximated as 8.99 × 10^9 N*m^2/C^2),
q1 and q2 are the charges of the particles, and
r is the distance between the particles.

In this case, we have:
q1 = +5.0 × 10^(-6) C (the first particle's charge)
q2 = +3.0 × 10^(-6) C (the second particle's charge)
r = 0.002 meters (the distance between the particles)

Now we can plug in the values and calculate the electric force:
F = (8.99 × 10^9 N*m^2/C^2) * ((|5.0 × 10^(-6) C| * |3.0 × 10^(-6) C|) / (0.002 meters)^2)

Step 3: Calculate the magnitude and direction of the electric force.
After calculating the above expression, you will get the value of the electric force in Newtons (N). The magnitude of the force is the absolute value of that result.

To determine the direction of the force, you need to consider the charges of the particles. If the charges are of the same sign, the force will be repulsive, pushing the particles away from each other. If the charges are of opposite signs, the force will be attractive, pulling the particles towards each other. In this case, since both charges are positive, the force will be repulsive.

Therefore, the magnitude of the electric force is the value you obtained, and the direction is away from the second particle (to the left).

Note: Make sure to keep track of the units throughout the calculations and final answer to ensure accuracy.