A positive charge of q = 2.6 µC is pulled on by two negative charges. As shown below, one, −2.0 µC, is 0.050 m to the north and the other, −4.0 µC, is d = 0.029 m to the south. What total force is exerted on the positive charge?
The two negative charges pull the positive charge in opposite directions. Use Coulomb's law
F = k q1 q2 /r^2
to compute the two separate forces. The force pulling to the south will be stronger because the -4.0 uC charge is larger and closer. Subtract the force due to the other charge to get the total force, which will be the south.
To calculate the total force exerted on the positive charge, we can use Coulomb's Law. Coulomb's Law 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.
The formula for the force between two charges is:
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,
r is the distance between the charges.
Let's calculate the forces individually for each pair of charges and then add them up:
1. Force between the positive charge (q = 2.6 µC) and the negative charge (-2.0 µC):
F1 = k * (q1 * q2) / r^2
= (9 x 10^9 Nm^2/C^2) * ((2.6 x 10^(-6) C) * (-2.0 x 10^(-6) C)) / (0.050 m)^2
= (9 x 10^9) * (2.6 x 10^(-6)) * (-2.0 x 10^(-6)) / (0.050)^2
2. Force between the positive charge (q = 2.6 µC) and the other negative charge (-4.0 µC):
F2 = k * (q1 * q2) / r^2
= (9 x 10^9 Nm^2/C^2) * ((2.6 x 10^(-6) C) * (-4.0 x 10^(-6) C)) / (0.029 m)^2
= (9 x 10^9) * (2.6 x 10^(-6)) * (-4.0 x 10^(-6)) / (0.029)^2
Now, we can calculate the total force exerted on the positive charge by summing up the individual forces:
Total force = F1 + F2
Note: Since one of the forces is acting to the north and the other is acting to the south, we need to consider their directions as well.
To find the total force exerted on the positive charge, we can use Coulomb's law, which states that the force between two charges is given by:
F = k * |q1 * q2| / r^2
Where:
- F is the force between the charges
- k is the Coulomb's constant (k = 8.99 * 10^9 N·m^2/C^2)
- q1 and q2 are the magnitudes of the charges
- r is the distance between the charges
In this scenario, the positive charge is being pulled by two negative charges. We need to first find the forces exerted by each negative charge individually, and then add them to get the total force.
Let's calculate the force exerted by the first negative charge:
q1 = -2.0 µC (charge of the first negative charge)
q2 = 2.6 µC (charge of the positive charge)
r1 = 0.050 m (distance between the first negative charge and the positive charge)
Using Coulomb's law, we have:
F1 = k * |q1 * q2| / r1^2
Now, let's calculate the force exerted by the second negative charge:
q1 = -4.0 µC (charge of the second negative charge)
q2 = 2.6 µC (charge of the positive charge)
r2 = 0.029 m (distance between the second negative charge and the positive charge)
Using Coulomb's law, we have:
F2 = k * |q1 * q2| / r2^2
Finally, the total force exerted on the positive charge is the sum of the individual forces:
Total Force = F1 + F2