How Do You Calculate Electric Fields and Forces Between Multiple Point Charges?

[squissv]

I could really use some help with the following question:

Three point charges are located as follows: q1= (0,0) m, q2= (0,-0.120) m, q3= (0.272,0) m. Take q1= 4.37 x 10-9 C, q2= -3.00 x 10-9 C, q3= 6.41 x 10-9 C.

a) Find the vector electric field that the q2 and q3 charges together create at the origin. What are the x- and y-components of the electric field?

b) Find the vector force on the q1 charge. What are the x- and y-components of the force?

I have tried using the summation of Coulomb's Law and a dozen other approaches, that I can't really describe because they were so haphazard. Any help would be greatly appreciated. Thanks!

 

[dynamicsolo]

It will really be helpful to draw a diagram of this situation first. They have actually been very nice to you in having you figure out distances and components by placing q2 and q3 right on the x- or y-axis. (Most problems are not so tidy...)

Which way will the fields from q2 and q3 point at the origin? What are the distances of those charges from the origin? Do the charges produce two field components each?

 

[Moetasim]

I would suggest approaching this problem by breaking it down into smaller parts and using the principles of electrostatics to solve each part individually. Firstly, we can calculate the electric field at the origin due to q2 and q3 using the formula for electric field: E = k * q / r^2, where k is the Coulomb's constant (8.99 x 10^9 Nm^2/C^2), q is the charge, and r is the distance from the charge to the point where the electric field is being calculated. In this case, we have two charges (q2 and q3) creating the electric field, so we can use vector addition to find the total electric field at the origin.

For q2, the distance from the origin is 0.120 m and the charge is -3.00 x 10^-9 C. Plugging these values into the formula, we get an electric field of -2.49 x 10^5 N/C directed towards the origin in the y-direction.

For q3, the distance from the origin is 0.272 m and the charge is 6.41 x 10^-9 C. Using the same formula, we get an electric field of 7.10 x 10^5 N/C directed away from the origin in the x-direction.

To find the total electric field at the origin, we can use vector addition by adding the x- and y-components of the electric fields from q2 and q3. This will give us a total electric field of 7.10 x 10^5 N/C in the x-direction and -2.49 x 10^5 N/C in the y-direction.

For part b, we can use the formula for the electric force: F = k * q1 * q2 / r^2, where q1 is the charge experiencing the force, q2 is the charge creating the field, and r is the distance between the two charges. In this case, q1 is located at the origin and q2 is located at (-0.120, 0) m. Using the same values for k and q2 as before, we can calculate the force on q1 to be 1.35 x 10^-3 N directed towards q2 in the x-direction.

I understand that this problem may have been challenging, but it's important to approach it systematically and use the principles