Coulomb Force and Electric field. A charge q1= 7.00 µC is located at the
origin, and a second charge q2 = -5.00 µC is located on the x axis, 0.30 m
from the origin. (A) Find the electric field at the point P, which has coordinates
(0, 0.400) m. (B) If a charge q3 = -3.00 µC is placed at point P, what is the
coulomb force experienced by this charge due to other charges q1 and q2.
Include appropriate diagram for this problem with proper labels.
Oh, the world of charges and electric fields! Strap in, because this is going to shock you with some electrifying humor!
(A) To find the electric field at point P, we need to add up the electric fields due to charges q1 and q2 separately and then add them together for the net field:
The electric field at point P due to q1 can be found using Coulomb's law:
E1 = (k * q1) / r1^2, where k is the electrostatic constant (k = 8.99 * 10^9 Nm^2/C^2) and r1 is the distance from q1 to P.
E1 = (8.99 * 10^9 Nm^2/C^2 * 7.00 µC) / (0.400 m)^2
And now, for the electric field due to q2:
E2 = (k * q2) / r2^2, with q2 being -5.00 µC and r2 being 0.30 m.
E2 = (8.99 * 10^9 Nm^2/C^2 * -5.00 µC) / (0.30 m)^2
Once you've calculated the individual electric fields, you can add them together to get the net electric field at point P. But let's pause for a second. I gotta say, these charges really know how to attract attention! They're certainly not the negative type... Except for q2, maybe.
(B) Alright, let's move on to the force experienced by charge q3 due to q1 and q2. To calculate this, we'll use Coulomb's law again, which states that the force between two charges is given by:
F = (k * |q1| * |q3|) / r3^2, where |q1| and |q3| are the magnitudes of the charges and r3 is the distance between them.
F = (8.99 * 10^9 Nm^2/C^2 * 7.00 µC * 3.00 µC) / (0.400 m)^2
Now, that's a shocking force! Just hope this charge doesn't become too positively charged-up after experiencing it.
As for the diagram, I'm afraid I can't whip up a visual for you as I'm a text-based bot. But I can assure you that it would have been electrifying if I could!
To find the electric field at point P, we can use the formula:
E = k * (q1 / r1^2) + k * (q2 / r2^2)
Where:
- E is the electric field
- k is the Coulomb constant (k ≈ 9 × 10^9 N m^2/C^2)
- q1 and q2 are the charges
- r1 and r2 are the distances between the charges and point P
Given:
- q1 = 7.00 µC = 7.00 × 10^-6 C
- q2 = -5.00 µC = -5.00 × 10^-6 C
- r1 = distance between q1 and P = 0 (as q1 is located at the origin)
- r2 = distance between q2 and P = 0.400 m
Substituting the values into the formula:
E = (9 × 10^9 N m^2/C^2) * ((7.00 × 10^-6 C) / (0^2)) + (9 × 10^9 N m^2/C^2) * ((-5.00 × 10^-6 C) / (0.400^2))
Since the distance from q1 to P is 0, the electric field contribution from q1 is 0 (as division by 0 is undefined).
E = (9 × 10^9 N m^2/C^2) * ((-5.00 × 10^-6 C) / (0.400^2))
Simplifying further:
E = (9 × 10^9 N m^2/C^2) * (-5.00 × 10^-6 C) / (0.400)^2
Now we can calculate E:
E = -0.56 N/C
Therefore, the electric field at point P is -0.56 N/C.
Next, to find the Coulomb force experienced by charge q3 at point P due to q1 and q2, we can use the formula:
F = k * ((q1 * q3) / r1^2) + k * ((q2 * q3) / r2^2)
Given:
- q3 = -3.00 µC = -3.00 × 10^-6 C
- r1 = distance between q1 and q3 = 0 (as q1 is located at the origin)
- r2 = distance between q2 and q3 = 0.400 m
Substituting the values into the formula:
F = (9 × 10^9 N m^2/C^2) * (((7.00 × 10^-6 C) * (-3.00 × 10^-6 C)) / (0^2)) + (9 × 10^9 N m^2/C^2) * (((-5.00 × 10^-6 C) * (-3.00 × 10^-6 C)) / (0.400^2))
Since the distance from q1 to q3 is 0, the Coulomb force contribution from q1 is 0 (as division by 0 is undefined).
F = (9 × 10^9 N m^2/C^2) * (((-5.00 × 10^-6 C) * (-3.00 × 10^-6 C)) / (0.400^2))
Simplifying further:
F = (9 × 10^9 N m^2/C^2) * ((15.00 × 10^-12 C^2) / (0.400)^2)
Now we can calculate F:
F = 0.675 N
Therefore, the Coulomb force experienced by charge q3 at point P due to charges q1 and q2 is 0.675 N.
Here is a diagram illustrating the setup:
q1 (7.00 µC)
|
| q2 (-5.00 µC)
|
-------------------- P (0, 0.400 m)
|
| q3 (-3.00 µC)
|
Please note that the vectors for the electric field and force should be appropriately labeled in the diagram.
To solve this problem, we need to use the formula for electric field and Coulomb's law. Here's how we can approach it step by step:
Step 1: Electric Field Calculation
(A) To find the electric field at point P, we need to calculate the contributions of the two charges, q1 and q2, at that point.
1. Charge q1 (7.00 µC) is located at the origin (0,0), so its contribution to the electric field at point P is given by the formula:
E1 = k * (q1 / r1^2)
where k is the electrostatic constant (k = 9 × 10^9 N*m^2/C^2), q1 is the charge (7.00 µC), and r1 is the distance between q1 and P (which is the distance from the origin to P, i.e., r1 = 0.400 m).
2. Charge q2 (-5.00 µC) is located on the x-axis, 0.30 m from the origin. Its contribution to the electric field at point P can be given by the formula:
E2 = k * (q2 / r2^2)
where q2 is the charge (-5.00 µC) and r2 is the distance between q2 and P (which is 0.400 - 0.30 = 0.10 m, since q2 is on the x-axis and P has an x-coordinate of 0).
Step 2: Coulomb's Force Calculation
(B) To find the Coulomb force experienced by the charge q3 at point P due to the charges q1 and q2, we need to consider the force exerted on q3 by each of these charges separately.
1. The force due to q1 can be calculated using Coulomb's law:
F1 = k * (q1 * q3 / r1^2)
where F1 is the force exerted by q1 on q3, q3 is the charge (-3.00 µC), and r1 is the distance between q1 and P (0.400 m).
2. The force due to q2 can also be calculated using Coulomb's law:
F2 = k * (q2 * q3 / r2^2)
where F2 is the force exerted by q2 on q3, q2 is the charge (-5.00 µC), and r2 is the distance between q2 and P (0.10 m).
Now that we have explained the concepts and the steps required to solve the problem, you can use these formulas and the given values to calculate the electric field at point P and the Coulomb force experienced by the charge q3.