Please Help,
Two point charges are fixed on the y axis: a negative point charge q1 = -23 µC at y1 = +0.23 m and a positive point charge q2 at y2 = +0.33 m. A third point charge q = +7.8 µC is fixed at the origin. The net electrostatic force exerted on the charge q by the other two charges has a magnitude of 29 N and points in the +y direction. Determine the magnitude of q2.
Add up the two forces acting on q, using the Coulomb equation for the forces due to q1 and q2, and solve for the only unknown, q1.
The force due to q2 acting upn q is up (+y)and the force due to q1 on q is down (-y).
Show your work if further assistance is needed.
Well, looks like we have a shocking situation here! Let's see if we can crack it with some electrifying humor!
To solve this problem, we need to use Coulomb's Law, which 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. In equation form, it looks like this:
F = k * (|q1| * |q2|) / r^2,
where F is the force, k is the electrostatic constant, q1 and q2 are the charges, and r is the distance between them.
Now, let's do some calculations and zap our way to the answer!
Given:
q1 = -23 µC at y1 = +0.23 m
q2 = ? (we're trying to find this)
q = +7.8 µC at the origin
F = 29 N in the +y direction
First, we need to calculate the distance between q1 and q:
r1 = sqrt((0 - 0.23)^2) = 0.23 m.
And the distance between q2 and q:
r2 = sqrt((0.33 - 0)^2 + (0 - 0)^2) = 0.33 m.
Now, we can plug these values into Coulomb's Law:
29 = k * (|q1| * |q2|) / (0.23)^2,
29 = k * (23 µC * |q2|) / (0.23)^2.
Simplifying this equation, multiplying both sides by (0.23)^2 and dividing by 23 µC:
|q2| = 29 * (0.23)^2 / 23,
|q2| = 0.0678 C.
So, the magnitude of q2 is 0.0678 C.
And there you have it! With a touch of humor and a jolt of calculation, we've solved the problem! Keep those questions coming, and I'll be here to brighten up your day!
To determine the magnitude of q2, we need to use Coulomb's Law and principles of vectors.
Coulomb's Law states that the magnitude of the electrostatic force between two point charges is given by:
F = (k * |q1 * q2|) / r^2
Where:
- F is the electrostatic force
- k is 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 case, we have three charges: q1, q2, and q. The net force exerted on q by the other two charges is given as 29 N and points in the +y direction.
Let's analyze the situation:
1. Determine the electrostatic force between q1 and q:
The force exerted on q by q1 can be written as:
F1 = (k * |q1 * q|) / r1^2
Since we know that the force points in the +y direction, we can write:
F1 = -29 N (since it is negative for the force to be in the +y direction)
Substituting the known values, we have:
-29 N = (k * |(-23 µC)(7.8 µC)|) / (0.23 m)^2
Simplifying, we find:
(-23 µC)(7.8 µC) = (-29 N)(0.23 m)^2 / k
Now, we can evaluate (-23 µC)(7.8 µC) = -179.4µC^2
Substituting the known values, we have:
-179.4µC^2 = (-29 N)(0.23 m)^2 / k
2. Determine the electrostatic force between q2 and q:
The force exerted on q by q2 can be written as:
F2 = (k * |q2 * q|) / r2^2
Since we know that the force points in the +y direction, we can write:
F2 = 29 N
Substituting the known values, we have:
29 N = (k * |q2 * 7.8 µC|) / (0.33 m)^2
Simplifying, we find:
(q2 * 7.8 µC) = (29 N)(0.33 m)^2 / k
Now, we can evaluate (29 N)(0.33 m)^2 = 308.07 N m^2 / C^2
Substituting the known values, we have:
(q2 * 7.8 µC) = 308.07 N m^2 / C^2 / k
3. Determine the magnitude of q2:
To find q2, we need to divide the equation we found in step 2 by the equation we found in step 1:
(q2 * 7.8 µC) / (-179.4µC^2) = (308.07 N m^2 / C^2 / k) / (-29 N)(0.23 m)^2 / k
Simplifying, we find:
q2 = (-179.4µC^2 * 308.07 N m^2 / C^2) / (-29 N * (0.23 m)^2)
Evaluating the expression, we find:
q2 ≈ 0.65 µC
Therefore, the magnitude of q2 is approximately 0.65 µC.
To determine the magnitude of q2, we can make use of Coulomb's Law, which states that the electrostatic force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
The formula for Coulomb's Law is:
F = (k * |q1 * q2|) / r^2
Where:
- F is the magnitude of the electrostatic force
- k is the electrostatic constant, which is approximately equal to 9 x 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 case, the electrostatic force is given, which is 29 N and it points in the +y direction. The charge, q, is also given, which is +7.8 µC.
We can start by finding the distance between the charge, q1, and the origin. Since q1 is on the y-axis at y1 = +0.23 m, the distance is simply y1.
r1 = y1 = +0.23 m
Next, we need to find the force between q and q1. Since the force is in the +y direction, the charges q and q1 must have opposite signs.
F = (k * |q * q1|) / r1^2
Substituting the given values:
29 N = (9 x 10^9 N*m^2/C^2) * (7.8 x 10^-6 C) * (-23 x 10^-6 C) / (0.23 m)^2
Now, we can solve for q2. Rearranging the equation, we get:
q2 = [(29 N) * (0.23 m)^2] / [(9 x 10^9 N*m^2/C^2) * (7.8 x 10^-6 C) * (23 x 10^-6 C)]
Plugging in the values and solving the equation will give us the magnitude of q2.