A negative charge Q1 = -20.0 mC is located at a point X1 = -2.00 m, a positive charge Q2 = 10.0 mC is located at a point X2 = 3.00 m and a positive charge Q3 = 30.0 mC is located at a point X3 = 9.0 m.a. Draw free body diagrams for the electric force acting on Q1, Q2, and Q3.b. Find the magnitude of the force between Q1 and Q2.c. Find the magnitude of the force between Q1 and Q3.d. Find the magnitude of the force between Q2 and Q3.e. Find the magnitude and direction of the net electric force on charge Q1.f. Find the magnitude and direction of the net electric force on charge Q2.g. Find the magnitude and direction of the net electric force on charge Q3.
a.
For Q1:
---------Q1
For Q2:
---------Q2
For Q3:
---------Q3
b. The magnitude of the force between Q1 and Q2 can be calculated using the formula:
F = k * |Q1| * |Q2| / r^2
where k is the electrostatic constant (k = 8.99 × 10^9 N m^2/C^2), |Q1| and |Q2| are the magnitudes of the charges, and r is the distance between the charges.
F = (8.99 × 10^9 N m^2/C^2) * (20.0 × 10^-3 C) * (10.0 × 10^-3 C) / (3.00 + 2.00)^2
c. The magnitude of the force between Q1 and Q3 can be calculated in a similar way:
F = k * |Q1| * |Q3| / r^2
F = (8.99 × 10^9 N m^2/C^2) * (20.0 × 10^-3 C) * (30.0 × 10^-3 C) / (9.00 + 2.00)^2
d. The magnitude of the force between Q2 and Q3 can also be calculated in the same manner:
F = k * |Q2| * |Q3| / r^2
F = (8.99 × 10^9 N m^2/C^2) * (10.0 × 10^-3 C) * (30.0 × 10^-3 C) / (9.00 - 3.00)^2
e. The net electric force on charge Q1 can be found by considering the forces between Q1 and Q2, and between Q1 and Q3, using vector addition.
f. The net electric force on charge Q2 can be found by considering the forces between Q2 and Q1, and between Q2 and Q3, using vector addition.
g. The net electric force on charge Q3 can be found by considering the forces between Q3 and Q1, and between Q3 and Q2, using vector addition.
Sorry, I couldn't come up with a humorous response for this one! But I hope the explanations were helpful!
a.
- Free body diagram for Q1: The arrow representing the force should be directed towards Q2 and Q3 since Q1 is negatively charged.
- Free body diagram for Q2: The arrow representing the force should be directed towards Q1 since Q2 is positively charged.
- Free body diagram for Q3: The arrow representing the force should be directed towards Q1 since Q3 is positively charged.
b.
The magnitude of the force between two charges is given by Coulomb's Law: F = k * |Q1 * Q2| / r^2, where k is the electrostatic constant (k = 9.0 x 10^9 Nm^2/C^2). Plug in the values:
F = (9.0 x 10^9 Nm^2/C^2) * |(-20.0 mC) * (10.0 mC)| / (3.00 m - (-2.00 m))^2
c.
Using Coulomb's Law, plug in the values:
F = (9.0 x 10^9 Nm^2/C^2) * |(-20.0 mC) * (30.0 mC)| / (9.00 m - (-2.00 m))^2
d.
Using Coulomb's Law, plug in the values:
F = (9.0 x 10^9 Nm^2/C^2) * |(10.0 mC) * (30.0 mC)| / (9.00 m - 3.00 m)^2
e.
To calculate the net electric force on Q1, consider the magnitudes and directions of the forces acting on Q1. Since Q2 and Q3 are both positive charges, the forces on Q1 due to Q2 and Q3 will be in opposite directions. Use the principle of vector addition to find the net force.
f.
To calculate the net electric force on Q2, consider the magnitudes and directions of the forces acting on Q2. Since Q1 is negatively charged and Q3 is positively charged, the forces on Q2 due to Q1 and Q3 will be in opposite directions. Use the principle of vector addition to find the net force.
g.
To calculate the net electric force on Q3, consider the magnitudes and directions of the forces acting on Q3. Since Q1 and Q2 are both positively charged, the forces on Q3 due to Q1 and Q2 will be in the same direction. Use the principle of vector addition to find the net force.
a. To draw free body diagrams for the electric force acting on Q1, Q2, and Q3, we need to consider the interaction between them and the direction of the force.
For Q1:
- It experiences a repulsive force from Q2 since they have the same charge.
- It experiences an attractive force from Q3 since they have opposite charges.
- The force from Q2 is directed away from Q2 since they have the same charge.
- The force from Q3 is directed towards Q3 since they have opposite charges.
For Q2:
- It experiences an attractive force from Q1 since they have opposite charges.
- It experiences a repulsive force from Q3 since they have the same charge.
- The force from Q1 is directed towards Q1 since they have opposite charges.
- The force from Q3 is directed away from Q3 since they have the same charge.
For Q3:
- It experiences an attractive force from Q1 since they have opposite charges.
- It experiences a repulsive force from Q2 since they have the same charge.
- The force from Q1 is directed towards Q1 since they have opposite charges.
- The force from Q2 is directed away from Q2 since they have the same charge.
b. To find the magnitude of the force between Q1 and Q2, we can use Coulomb's Law:
F12 = (k * |Q1 * Q2|) / r^2
where k is the electrostatic constant, Q1 and Q2 are the charges, and r is the distance between the charges.
Substituting the given values, we have:
F12 = (8.99 x 10^9 N.m^2/C^2 * |(-20.0 x 10^-3 C) * (10.0 x 10^-3 C)|) / (3.00 m)^2
Calculating this expression will give us the magnitude of the force between Q1 and Q2.
c. Similarly, to find the magnitude of the force between Q1 and Q3, we can use Coulomb's Law:
F13 = (k * |Q1 * Q3|) / r^2
Using the given values, we can calculate F13.
d. To find the magnitude of the force between Q2 and Q3, we can once again use Coulomb's Law:
F23 = (k * |Q2 * Q3|) / r^2
By plugging in the given values, we can determine F23.
e. To find the magnitude and direction of the net electric force on charge Q1, we need to consider the individual forces acting on it (from Q2 and Q3) and sum them vectorially by taking into account their direction and magnitude.
f. Similarly, to find the magnitude and direction of the net electric force on charge Q2, we need to consider the individual forces acting on it (from Q1 and Q3) and sum them vectorially.
g. Finally, to find the magnitude and direction of the net electric force on charge Q3, we need to consider the individual forces acting on it (from Q1 and Q2) and sum them vectorially.