Three point charges are placed at the following points on the x- axis;+2uc at x=0,-3uc at x=40cm,-5uc at x=120cm.find the force on the -5uc charge.
To find the force on the -5uC charge, we need to calculate the forces between this charge and the other charges using Coulomb's law and then sum them up.
Coulomb's law states that the force between two charges is given by:
F = k * |q1 * q2| / r^2
where F is the force, k is the electrostatic constant (k = 9 × 10^9 N m^2/C^2), q1 and q2 are the charges, and r is the distance between them.
Let's calculate the force between the -5uC charge and the +2uC charge at x = 0:
q1 = -5uC
q2 = +2uC
r = 120cm - 0cm = 120cm = 1.2m
F1 = k * |q1 * q2| / r^2
= (9 × 10^9 N m^2/C^2) * |-5uC * 2uC| / (1.2m)^2
Now, let's calculate the force between the -5uC charge and the -3uC charge at x = 40cm:
q1 = -5uC
q2 = -3uC
r = 120cm - 40cm = 80cm = 0.8m
F2 = k * |q1 * q2| / r^2
= (9 × 10^9 N m^2/C^2) * |-5uC * -3uC| / (0.8m)^2
Finally, let's calculate the force between the -5uC charge and the +2uC charge at x = 120cm:
q1 = -5uC
q2 = +2uC
r = 120cm - 120cm = 0cm = 0m
F3 = k * |q1 * q2| / r^2
= (9 × 10^9 N m^2/C^2) * |-5uC * 2uC| / (0m)^2
To find the total force on the -5uC charge, we sum up the forces:
Total force = F1 + F2 + F3
I'll calculate the values for you.
To find the force on the -5 μC charge, we will apply Coulomb's Law, which states that the force between two point charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them.
The formula for Coulomb's Law is:
F = k * (|q1| * |q2|) / r^2
Where:
- F is the force between the charges,
- k is Coulomb's constant (approximately 9 × 10^9 Nm^2/C^2),
- |q1| and |q2| are the magnitudes of the charges, and
- r is the distance between the charges.
In this case, we have three charges: +2 μC at x = 0, -3 μC at x = 40 cm, and -5 μC at x = 120 cm. We need to find the force on the -5 μC charge.
Step 1: Calculate the distances between the charges:
- The distance between the charges of -5 μC and -3 μC is 120 cm - 40 cm = 80 cm.
- The distance between the charges of -5 μC and +2 μC is 120 cm - 0 cm = 120 cm.
Step 2: Convert the distances to meters:
- 80 cm = 0.8 m
- 120 cm = 1.2 m
Step 3: Calculate the force between the -5 μC charge and the -3 μC charge:
F1 = k * (|-5 μC| * |-3 μC|) / (0.8 m)^2
Step 4: Calculate the force between the -5 μC charge and the +2 μC charge:
F2 = k * (|-5 μC| * |+2 μC|) / (1.2 m)^2
Step 5: Add the forces together to find the total force on the -5 μC charge:
Total Force = F1 + F2
Solving the above equations will give you the force on the -5 μC charge.