Two identical teflon rods are 10 centimeters long and rubbed with fur so that they each have a total negative charge of 20 microCoulombs that is uniformly distributed along their length. They are arranged along the same axis, with their ends 5 centimeters apart. What is the magnitude of the electrostatic force felt by each rod in Newtons?
To find the magnitude of the electrostatic force felt by each rod, we can use Coulomb's Law equation:
F = k * (|q1| * |q2|) / r^2
Where:
F is the electrostatic force,
k is the electrostatic constant (k = 9 * 10^9 Nm^2/C^2),
q1 and q2 are the charges on the rods, and
r is the distance between the rods.
In this case, since the rods have the same charge and are arranged along the same axis, the equation can be simplified to:
F = k * (|q|^2) / r^2
First, let's convert the given distance and charge values from centimeters and microCoulombs to meters and Coulombs respectively:
Length of the rods (r) = 10 centimeters = 0.1 meters
Charge on each rod (|q|) = 20 microCoulombs = 20 * 10^-6 Coulombs
Now we can substitute these values into the simplified equation:
F = (9 * 10^9 Nm^2/C^2) * ((20 * 10^-6 Coulombs)^2) / (0.1 meters)^2
Calculating this expression will give us the magnitude of the electrostatic force felt by each rod in Newtons.
To calculate the electrostatic force felt by each rod, we can use Coulomb's Law. Coulomb's Law states that the electrostatic force between two charged objects 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 problem into smaller steps:
Step 1: Determine the charge per unit length of the rods.
Since the rods are identical and have a uniform charge distribution, we can find the charge per unit length by dividing the total charge by the length of each rod:
Charge per unit length = Total charge / Length of the rod
Given that each rod has a total negative charge of 20 microCoulombs and a length of 10 centimeters, we can convert these values into SI units:
Total charge = 20 microCoulombs = 20 × 10^(-6) C
Length of the rod = 10 centimeters = 10 × 10^(-2) m
Now we can calculate the charge per unit length:
Charge per unit length = (Total charge) / (Length of the rod)
Step 2: Calculate the distance between the centers of the rods.
The ends of the rods are 5 centimeters apart, which means that the distance between their centers is equal to the sum of their lengths plus the distance between their ends:
Distance between the centers = 2 × (Length of the rod) + Distance between the ends
Distance between the ends = 5 centimeters = 5 × 10^(-2) m
Now we can calculate the distance between the centers of the rods:
Distance between the centers = 2 × (Length of the rod) + Distance between the ends
Step 3: Apply Coulomb's Law.
Now that we have the charge per unit length and the distance between the centers of the rods, we can use Coulomb's Law to find the electrostatic force felt by each rod.
Coulomb's Law formula: Electrostatic force = (k × (charge of rod 1) × (charge of rod 2)) / (distance between the centers)^2
Where:
- k is the electrostatic constant, with a value of 9 × 10^9 Nm^2/C^2
- charge of rod 1 and charge of rod 2 are the charges per unit length of each rod
Let's plug in the values and calculate the electrostatic force felt by each rod:
Electrostatic force = (k × (charge of rod 1) × (charge of rod 2)) / (distance between the centers)^2
Keep in mind that the force calculated will be the magnitude of the force, as the negative sign denotes the attraction between the rods.