Calculate the magnitude of the net electrostatic force on charge q1 due to the charges q2 and q3.
IF
q1= 3μ
distances from q1 to q2 is =0.10m
q2=-5μ
distances from q1 to q3 is =-0.15m
q3=-2μ
In simple steps
The formula to calculate the magnitude of the net electrostatic force between two charges q1 and q2 is given by Coulomb's Law:
F = k * |q1 * q2| / r^2
Where:
- F is the magnitude of the force
- k is Coulomb's constant, approximately 9 x 10^9 N*m^2/C^2
- q1 and q2 are the charges
- r is the distance between the two charges
For the force between charges q1 and q2:
F1 = (9 x 10^9 N*m^2/C^2) * |(3μC) * (-5μC)| / (0.10m)^2
Simplifying:
F1 = (9 x 10^9 N*m^2/C^2) * (15 x 10^-6 C^2) / (0.01m^2)
F1 = (9 x 10^9 N*m^2/C^2) * (1.5 x 10^-5 C^2) / (0.0001m^2)
F1 = (9 x 10^9 N*m^2/C^2) * (1.5 x 10^-1 N)
F1 = 1.35 x 10^9 N
For the force between charges q1 and q3:
F2 = (9 x 10^9 N*m^2/C^2) * |(3μC) * (-2μC)| / (0.15m)^2
Simplifying:
F2 = (9 x 10^9 N*m^2/C^2) * (6 x 10^-6 C^2) / (0.0225m^2)
F2 = (9 x 10^9 N*m^2/C^2) * (0.2666667 x 10^-4 C^2 / 0.0225)
F2 = (9 x 10^9 N*m^2/C^2) * (2.66667 x 10^-2 N)
F2 = 2.4 x 10^8 N
The net electrostatic force on charge q1 due to charges q2 and q3 is the vector sum of the two forces F1 and F2:
Net Force = F1 + F2
Net Force = 1.35 x 10^9 N + 2.4 x 10^8 N
Net Force = 1.59 x 10^9 N
Therefore, the magnitude of the net electrostatic force on charge q1 due to charges q2 and q3 is 1.59 x 10^9 N.
To calculate the magnitude of the net electrostatic force on charge q1 due to charges q2 and q3, you can use Coulomb's Law. Coulomb's Law states that the force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
Step 1: Determine the forces due to each charge (q2 and q3) individually.
- Force due to q2: Use the formula F = k * (q1 * q2) / r^2, where k is the electrostatic constant, q1 and q2 are the charges, and r is the distance between them.
- F2 = k * (q1 * q2) / r2^2
- F2 = (8.99 x 10^9 N m^2/C^2) * ((3 x 10^-6 C) * (-5 x 10^-6 C)) / (0.10 m)^2
- Force due to q3: Use the same formula as above but with the appropriate values.
- F3 = k * (q1 * q3) / r3^2
- F3 = (8.99 x 10^9 N m^2/C^2) * ((3 x 10^-6 C) * (-2 x 10^-6 C)) / (0.15 m)^2
Step 2: Calculate the net force by adding the forces due to q2 and q3.
- Net Force = F2 + F3
Step 3: Calculate the magnitude of the net force.
- Magnitude of Net Force = |Net Force|
Let's calculate the values step-by-step:
Step 1:
- F2 = (8.99 x 10^9 N m^2/C^2) * ((3 x 10^-6 C) * (-5 x 10^-6 C)) / (0.10 m)^2
- F2 = -1.35 x 10^-2 N (due to its negative sign)
- F3 = (8.99 x 10^9 N m^2/C^2) * ((3 x 10^-6 C) * (-2 x 10^-6 C)) / (0.15 m)^2
- F3 = -3.6 x 10^-3 N (due to its negative sign)
Step 2:
- Net Force = F2 + F3
- Net Force = -1.35 x 10^-2 N + -3.6 x 10^-3 N
- Net Force = -1.71 x 10^-2 N
Step 3:
- Magnitude of Net Force = |Net Force|
- Magnitude of Net Force = |-1.71 x 10^-2 N|
- Magnitude of Net Force = 1.71 x 10^-2 N
Therefore, the magnitude of the net electrostatic force on charge q1 due to charges q2 and q3 is 1.71 x 10^-2 N.
To calculate the magnitude of the net electrostatic force on charge q1 due to charges q2 and q3, we need to calculate the individual forces exerted by q2 and q3 on q1, and then add them together.
Step 1: Calculate the force between q1 and q2.
The force between two point charges can be calculated using Coulomb's Law:
F = (k * |q1 * q2|) / r^2
Where:
F is the force between the charges,
k is the electrostatic constant (k = 9 x 10^9 Nm^2/C^2),
|q1| and |q2| are the magnitudes of the charges, and
r is the distance between the charges.
Given that q1 = 3μC (microcoulombs), q2 = -5μC, and the distance from q1 to q2 is 0.10m, we can substitute these values into the formula:
F1 (force between q1 and q2) = (9 x 10^9 Nm^2/C^2 * |3μC * -5μC|) / (0.10m)^2
Step 2: Calculate the force between q1 and q3.
We use the same formula as above, but with the values of q1 = 3μC, q3 = -2μC, and the distance from q1 to q3 as -0.15m (note the negative sign indicating direction):
F2 (force between q1 and q3) = (9 x 10^9 Nm^2/C^2 * |3μC * -2μC|) / (0.15m)^2
Step 3: Calculate the net force on q1.
To find the net electrostatic force, we need to add F1 and F2 together:
Net force = F1 + F2
Now, let's substitute the calculated values into the equation and calculate the result.
Net force = F1 + F2