There is a 85uC point charge at the origin. Find the electric field at the point x3= -45cm , y3= 55cm
(5.85*10^5)(-.45+.75)/(-.45^2+.75^2)^3/2 am I totally off
The previous questions before this were to find at x1=40cm y1=0 and
x2=65cm y2=65cm
I figured those out, but can't get this one.
If you want the magnitude of E, you are way off.
E=Kq/r^2=k(.85E-6)/(.45^2+.75^2)
Now if you want E as E=Ex + Ey as a vector, you have to do it as a vector equation. I have no idea how you got the numbers and powers in the equation you typed.
To calculate the electric field at the point (x3, y3) due to a point charge at the origin, you can use the formula:
Electric field (E) = (k * Q) / r^2
Where:
- k is the Coulomb's constant (k = 8.99 * 10^9 N m^2/C^2)
- Q is the charge (in this case, Q = 8.5 * 10^-6 C)
- r is the distance from the origin to the point (x3, y3)
To find r, you can use the Pythagorean theorem:
r = sqrt((x3)^2 + (y3)^2)
Let's plug in the values and calculate step-by-step:
Given:
- Q = 8.5 * 10^-6 C
- x3 = -45 cm
- y3 = 55 cm
Convert the distances to meters:
- x3 = -0.45 m (since 1 cm = 0.01 m)
- y3 = 0.55 m (since 1 cm = 0.01 m)
Calculate r:
r = sqrt((-0.45)^2 + (0.55)^2)
= sqrt(0.2025 + 0.3025)
= sqrt(0.505)
≈ 0.71 m
Now, plug in the values into the electric field formula:
E = (k * Q) / r^2
= (8.99 * 10^9 N m^2/C^2) * (8.5 * 10^-6 C) / (0.71)^2
≈ 1.66 * 10^4 N/C
So, the electric field at the point (x3, y3) is approximately 1.66 * 10^4 N/C.
To find the electric field at a point due to a point charge, you can use the formula:
E = k * (q / r^2) * r_hat
Where:
- E is the electric field vector,
- k is the electrostatic constant (8.99 * 10^9 Nm^2/C^2),
- q is the charge of the point charge,
- r is the distance from the point charge to the point where you want to find the electric field,
- r_hat is the unit vector in the direction from the point charge to the point.
In this case, the point charge is located at the origin and has a charge of 85uC. The point where you want to find the electric field is at x3 = -45cm, y3 = 55cm.
To find the distance r between the point charge and the point of interest, you can use the distance formula:
r = sqrt((x3 - x1)^2 + (y3 - y1)^2)
Where (x1, y1) are the coordinates of the point charge.
Using the previous calculations you mentioned for x1 = 40cm, y1 = 0 and x2 = 65cm, y2 = 65cm, you can substitute these values into the formulas to find the values of r1 and r2.
Then, to find the magnitude of the electric field at each point, you can use the formula:
E = k * (q / r^2)
Using q = 85uC and r1, r2, you can calculate the magnitudes of the electric field at those points.
Finally, to find the electric field vector at the point (x3, y3), you can decompose the electric fields at points (x1, y1) and (x2, y2) into their x and y components, and then add the corresponding components together:
Ex_total = Ex1 + Ex2
Ey_total = Ey1 + Ey2
So, by calculating the magnitudes of the electric field at (x1, y1), (x2, y2) and combining them according to their x and y components, you can determine the electric field at (x3, y3).
I hope this explanation helps you understand the process of finding the electric field at the given point.