Consider the following three point charges arranged along the x-axis. (A.) q1 has a charge of -8.0x 10^-6 C and is located at x = -3.0m (b.) q2 carries a charge of 3.0x 10^-6 C and is located at the origin (C.) q3 has a charge of -4.0x 10^-6 C and is located at x = 3.0m. What is the overall force experienced by q2?
Well, when it comes to forces, it can get quite "charged"! But don't worry, I'm here to help you out.
To find the net force experienced by q2, we need to find the individual forces exerted on it by q1 and q3, and then add those forces together.
The formula to calculate the force between two point charges is given by Coulomb's Law:
F = (k * |q1 * q2|) / r^2
Where F is the force, k is Coulomb's constant (approximately 9 * 10^9 N m^2 / C^2), |q1| and |q2| are the magnitudes of the charges, and r is the distance between them.
Now, let's calculate the individual forces:
Force exerted on q2 by q1:
F1 = (k * |q1 * q2|) / r1^2
Given:
q1 = -8.0 * 10^-6 C
q2 = 3.0 * 10^-6 C
r1 = -3.0 m
Calculating F1:
F1 = (9 * 10^9 N m^2 / C^2) * |(-8.0 * 10^-6 C) * (3.0 * 10^-6 C)| / (-3.0 m)^2
F1 = ...Okay, let me crunch the numbers here...
F1 = 3.2 * 10^-3 N (approximately)
Now, let's calculate the force exerted on q2 by q3:
F3 = (k * |q2 * q3|) / r3^2
Given:
q2 = 3.0 * 10^-6 C
q3 = -4.0 * 10^-6 C
r3 = 3.0 m
Calculating F3:
F3 = (9 * 10^9 N m^2 / C^2) * |(3.0 * 10^-6 C) * (-4.0 * 10^-6 C)| / (3.0 m)^2
F3 = ...Give me a second to calculate...
F3 = 1.2 * 10^-3 N (approximately)
Now, to find the net force on q2, we can add these forces together:
Net Force = F1 + F3
Net Force = 3.2 * 10^-3 N + 1.2 * 10^-3 N
Net Force = ...Drumroll, please...
Net Force = 4.4 * 10^-3 N (approximately)
So, the overall force experienced by q2 is 4.4 * 10^-3 N. I hope this "charged" answer puts a positive spin on your day!
To find the overall force experienced by q2, we need to calculate the individual forces between q2 and q1 and q2 and q3, and then add them together.
Here's how you can do it step by step:
Step 1: Find the distance between q2 and q1.
The distance between q2 (which is at the origin) and q1 (at x = -3.0m) is simply the absolute value of the x-coordinate of q1, which is 3.0m.
Step 2: Calculate the force between q2 and q1.
The force (F1) between two point charges can be calculated using Coulomb's Law:
F1 = (k * |q1 * q2|) / r^2
where k is the Coulomb's constant (9.0 x 10^9 N m^2/C^2), q1 and q2 are the charges of the respective particles, and r is the distance between them.
In this case, q1 = -8.0 x 10^-6 C, q2 = 3.0 x 10^-6 C, and r = 3.0m.
Substituting the values into the formula, we get:
F1 = (9.0 x 10^9 N m^2/C^2 * |-8.0 x 10^-6 C * 3.0 x 10^-6 C|) / (3.0m)^2
Step 3: Find the direction of the force between q2 and q1.
Since q1 has a negative charge and is located to the left of q2, the force between them will be repulsive (since opposite charges attract), and it will act in the positive x-direction.
Step 4: Repeat steps 1-3 for q2 and q3.
Step 5: Add the forces together.
Since forces are vector quantities, we need to consider their magnitudes and directions. If the forces have the same direction, we simply add their magnitudes. If they have opposite directions, we subtract their magnitudes.
Finally, the overall force experienced by q2 is the vector sum of the forces F1 and F2.
To find the overall force experienced by q2, we need to calculate the individual forces exerted on q2 by q1 and q3, and then combine them using vector addition.
The force between two point charges 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 (9.0 x 10^9 Nm^2/C^2),
|q1| and |q2| are the magnitudes of the charges,
and r is the distance between the charges.
Let's calculate the forces exerted on q2 by q1 and q3 separately:
1. Force exerted by q1 on q2:
|q1| = 8.0 x 10^-6 C (magnitude of charge q1)
|r1| = 3.0 m (distance between q1 and q2)
Using Coulomb's law:
F1 = k * (|q1| * |q2|) / |r1|^2
F1 = (9.0 x 10^9 Nm^2/C^2) * ((8.0 x 10^-6 C) * (3.0 x 10^-6 C)) / (3.0 m)^2
F1 = 64.0 x 10^-9 N
2. Force exerted by q3 on q2:
|q3| = 4.0 x 10^-6 C (magnitude of charge q3)
|r3| = 3.0 m (distance between q3 and q2)
Using Coulomb's law:
F3 = k * (|q3| * |q2|) / |r3|^2
F3 = (9.0 x 10^9 Nm^2/C^2) * ((4.0 x 10^-6 C) * (3.0 x 10^-6 C)) / (3.0 m)^2
F3 = 72.0 x 10^-9 N
Now, to find the overall force, we need to consider the direction of the forces. Since q1 is negatively charged (q1 = -8.0 x 10^-6 C) and q3 is also negatively charged (q3 = -4.0 x 10^-6 C), the forces F1 and F3 will be attractive forces towards q2.
To combine the forces, we add them since they act in the same direction:
F_overall = F1 + F3
F_overall = 64.0 x 10^-9 N + 72.0 x 10^-9 N
F_overall = 136.0 x 10^-9 N
Thus, the overall force experienced by q2 is 136.0 x 10^-9 N, directed towards q2.