Q.3 Three point charges are placed at the following points on x-axis: 3µC at x=0, -4µC at x=50cm and
-5µC at x=120cm. Calculate the force on -4µC charge.
At 50 the force on Q2 is to the left (attractive) from Q1 and to the left (repulsive) from Q3 so they add and are in the -x direction.
F = -k * 4µC [ 3µC/0.50^2 + 5µC/0.70^2 ]
To calculate the force on the -4µC charge, we need to use Coulomb's law which 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 them.
Here are the steps to calculate the force:
Step 1: Convert the distances to meters.
- x=50cm = 0.50m
- x=120cm = 1.20m
Step 2: Calculate the distance between the -4µC charge and the other charges.
- The distance between the -4µC charge and the 3µC charge is 0.50m.
- The distance between the -4µC charge and the -5µC charge is 1.20m.
Step 3: Calculate the force between the -4µC charge and the 3µC charge using Coulomb's law formula:
- F1 = (k * |q1 * q2|) / r^2
- where F1 is the force, k is the electrostatic constant (9 x 10^9 Nm^2/C^2), q1 is the charge of the -4µC charge, q2 is the charge of the 3µC charge, and r is the distance between them.
Substituting the values:
- F1 = (9 x 10^9 Nm^2/C^2) * (|-4µC * 3µC|) / (0.50m)^2
Step 4: Calculate the force between the -4µC charge and the -5µC charge using Coulomb's law formula:
- F2 = (k * |q1 * q2|) / r^2
- where F2 is the force, k is the electrostatic constant (9 x 10^9 Nm^2/C^2), q1 is the charge of the -4µC charge, q2 is the charge of the -5µC charge, and r is the distance between them.
Substituting the values:
- F2 = (9 x 10^9 Nm^2/C^2) * (|-4µC * -5µC|) / (1.20m)^2
Step 5: Add the two forces together to find the total force on the -4µC charge:
- Total force = F1 + F2
Now, you can calculate the force on the -4µC charge by substituting the values into the formulas and performing the calculations.
To calculate the force on the -4µC charge, we can use the principle of electrostatics. The force between two charges can be calculated using Coulomb's Law, which states that the force between two charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them.
Let's denote the -4µC charge as q1, and the other charges as q2 and q3. The force between q1 and q2 can be calculated as:
F12 = (k * |q1| * |q2|) / (r12)^2
where:
k is the electrostatic constant (8.99 × 10^9 N·m²/C²)
|q1| and |q2| are the magnitudes of the charges
r12 is the distance between the charges
Similarly, the force between q1 and q3 can be calculated as:
F13 = (k * |q1| * |q3|) / (r13)^2
To find the net force on q1 due to the other charges, we need to calculate the individual forces F12 and F13 and add them.
Now let's substitute the given values:
|q1| = |-4µC| = 4µC
|q2| = |-5µC| = 5µC
|q3| = |3µC| = 3µC
r12 = distance between q1 and q2 = 50cm = 0.5m
r13 = distance between q1 and q3 = 120cm = 1.2m
Now, we can calculate the individual forces:
F12 = (8.99 × 10^9 N·m²/C² * 4µC * 5µC) / (0.5m)^2
F13 = (8.99 × 10^9 N·m²/C² * 4µC * 3µC) / (1.2m)^2
Simplifying these calculations will give us the values for F12 and F13.
Finally, the net force on q1 can be found by summing up the individual forces: Fnet = F12 + F13.
These calculations will give us the force on the -4µC charge due to the other charges placed on the x-axis.