What Forces Act on a Charge at the Corner of a Rectangle?

[october2118]

Homework Statement

Four charges are placed on the corners of a rectangle. What is the resultant force on the positive charge (a = 1.4 m, b = 0.9 m, q = 2.7 × 10-9C)?

the rectangle has a charge
-q____-q
-q____+q on the 4 corners of the rectangle ant a line r from the +q to the -q diagonally
the bottom is labeled a and the left side is labeled b

Homework Equations

kq/ r^2
Fx and Fy components

The Attempt at a Solution

i started by using k and q 8.99*10^9 * 2.7*10^-9

then i divided it by the values of a and b and r which i got by using tan inverse of 1.4/ .9 i got my three numbers

-8.091*10^-8 x component
-3.34*10^-8 y component
-2.3499*10^-8 both

and since there is only 2 to add together for each i found F of x and y by multiplying by sin theta which is 32.74 degrees for the y components and cos theta for x components

next i found those numbers and plugged it into the formula F = square root of Fx^2 + Fy^2 and i got 7.143*10^-8 which is wrong i don't know where i went wrong

thanks

 

[turin]

The Coulomb froce law incorporates a product of two charges; you only have one.

The diagonal distance should be obtained from the Pythagorean theorem; inverse tangent will give you an angle.

I have no idea what you did after that.

There are three Coulomb forces acting on the positive charge. Determine them, and then add them up vectorially. Try to work it out symbolically, first.

 

[nlightner]

for your solution, but as a scientist, I would like to suggest a few improvements to your approach. Firstly, it is important to clearly define the problem and all relevant variables before attempting a solution. In this case, it would be helpful to specify the position and magnitude of each charge on the rectangle, as well as the distance between the positive charge and each of the other charges. This will allow for a more accurate and precise calculation.

Additionally, it is important to use consistent units throughout the calculation. In your attempt, it appears that you used meters for distance and coulombs for charge, but then used degrees for the angle. It would be more accurate to use radians for the angle, as it is a unitless quantity.

Furthermore, I would suggest using vector notation to represent the forces instead of breaking them down into components. This will make the calculation more straightforward and avoid any confusion with signs and directions.

Finally, it is always a good practice to double check your calculations and units to ensure accuracy. If you are still getting an incorrect result, it would be helpful to provide your calculations and any specific areas where you are unsure. This will allow for a more thorough analysis and potential corrections to your approach.