Charged spheres A and B are in fixed positions (like in question #6) and have charges 3.6x10^-6 C and -5.4x10^-6 C respectively. Calculate the net force on sphere C, which has a charge of -9.9x10^-6 C.
Well, it seems like sphere C is in quite a shocking situation! Let's see what the charges are up to.
The formula to calculate the electric force between two charges is given by Coulomb's Law:
F = (k * |q1 * q2|) / r^2
Where F is the force between the charges, k is a constant (k ≈ 9.0 × 10^9 N m²/C²), q1 and q2 are the charges, and r is the distance between the charges.
Since we have fixed positions for the charges, we can consider the forces between pairs of charges.
The force between A and C would be F_AC = (k * |q_A * q_C|) / r_AC^2.
The force between B and C would be F_BC = (k * |q_B * q_C|) / r_BC^2.
Now, let's analyze the net force acting on C. Since F is a vector, we must consider the signs properly.
F_net = F_AC + F_BC
F_AC = (k * |q_A * q_C|) / r_AC^2 = (9.0 × 10^9 * |3.6x10^-6 * -9.9x10^-6|) / r_AC^2
F_BC = (k * |q_B * q_C|) / r_BC^2 = (9.0 × 10^9 * |-5.4x10^-6 * -9.9x10^-6|) / r_BC^2
C comes into play with its own charge, but let's not get too clingy with too many calculations. Just plug in the numbers, and you'll get the answer.
Keep in mind that if you need the direction, you must pay attention to the signs of the forces and the position of the charges.
To calculate the net force on sphere C, we need to find the individual forces between sphere C and spheres A and B, and then add them together. The formula to calculate the force between two charged objects is given by Coulomb's Law:
F = k * (|q1| * |q2|) / r^2
Where F is the force between the charges, k is the electrostatic constant, |q1| and |q2| are the magnitudes of the charges, and r is the distance between the charges.
Let's go through the steps to calculate the net force on sphere C:
Step 1: Calculate the force between sphere C and sphere A.
Given:
Charge of sphere C, q1 = -9.9x10^-6 C
Charge of sphere A, q2 = 3.6x10^-6 C
Substituting these values into the formula:
F1 = k * (|q1| * |q2|) / r^2
Step 2: Calculate the force between sphere C and sphere B.
Given:
Charge of sphere C, q1 = -9.9x10^-6 C
Charge of sphere B, q2 = -5.4x10^-6 C
Substituting these values into the formula:
F2 = k * (|q1| * |q2|) / r^2
Step 3: Add the forces together to calculate the net force on sphere C.
Net force = F1 + F2
Note: To make the calculation more straightforward, you may use the value of Coulomb's constant, k = 9x10^9 N·m^2 / C^2.
Please provide the distance between the spheres to proceed with the calculation.
To calculate the net force on sphere C, we need to find the individual forces exerted on it by spheres A and B, and then add them together.
The force between two charged objects can be calculated using Coulomb's law:
F = (k * q1 * q2) / r^2
Where:
- F is the force between the two charges
- k is the Coulomb's constant (9 × 10^9 N * m^2 / C^2)
- q1 and q2 are the magnitudes of the charges on the objects
- r is the distance between the centers of the objects
First, let's calculate the force between sphere A and sphere C. We can assume that sphere B is at a certain distance from sphere C.
Let's say the distance rAC between spheres A and C is 1 meter.
Substituting the values into Coulomb's law equation:
FAC = (9 × 10^9 N * m^2 / C^2) * (3.6 × 10^-6 C) * (-9.9 × 10^-6 C) / (1 m)^2
Calculating this, we get:
FAC = (-32.4 N)
Note that the negative sign indicates that the force exerted by sphere A on sphere C is attractive.
Now, let's calculate the force between sphere B and sphere C. Again, we assume a distance rBC for this calculation.
Let's say the distance rBC between spheres B and C is 2 meters.
Substituting the values into Coulomb's law equation:
FBC = (9 × 10^9 N * m^2 / C^2) * (-5.4 × 10^-6 C) * (-9.9 × 10^-6 C) / (2 m)^2
Calculating this, we get:
FBC = (53.73 N)
Since sphere B has a negative charge and sphere C has a negative charge, the force between them is repulsive. Therefore, the force FBC is positive.
Finally, to find the net force on sphere C, we add the forces FAC and FBC:
Net Force on C = FAC + FBC
= (-32.4 N) + (53.73 N)
= 21.33 N
So, the net force on sphere C is 21.33 N.