HELP Need answer to this force due to charge problem

[matt85]

HELP! Need answer to this force due to charge problem!

Here it is:

Three charges are fixed in place as shown. The squares in the grid have sides of length s = 0.24 m. The magnitude of q is 3 mu or micro Coulombs (1 mu or micro Coulomb = 10-6 Coulombs), while the magnitude of Q is 4.5 mu or micro Coulombs. What is the magnitude of the net force on q due to the other two charges?

I really need the answer to the problem, it's killing me, I've worked on it for 2 hours and can't get it. The picture is attached.

Thanks a ton,
Matt

https://www.physicsforums.com/attachment.php?attachmentid=6103&stc=1&d=1137281964

 

[Astronuc]

How about writing the formula for electric force, and then putting in the numbers. Remember, the force and electric field are vector quantities, so one must use vector addition.

 

[quicknote]

Hi Matt,

I understand that this problem may be challenging for you, but it's important to remember that scientific problems often require patience and persistence. It's also important to not get too frustrated and ask for help when needed.

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 charges and inversely proportional to the square of the distance between them. In equation form, it is written as F = k(qQ)/r^2, where k is a constant equal to 8.99 x 10^9 Nm^2/C^2, q and Q are the two charges, and r is the distance between them.

In this case, we have three charges, q and Q are given, and we need to find the net force on q due to the other two charges. To do this, we can break the problem into two parts: the force between q and the charge at the top (Q1), and the force between q and the charge at the bottom (Q2).

Using Coulomb's Law, we can calculate the force between q and Q1 as F1 = k(qQ1)/r1^2, where r1 is the distance between them. Similarly, the force between q and Q2 is F2 = k(qQ2)/r2^2, where r2 is the distance between them.

Now, we need to find the total force on q, which is the vector sum of F1 and F2. Since the two forces are acting in opposite directions, we can simply subtract F2 from F1 to get the net force, Fnet = F1 - F2.

To find the distances, we can use the Pythagorean theorem. The distance between q and Q1 is equal to the length of the diagonal of the square, which is s√2. Similarly, the distance between q and Q2 is also s√2. Plugging in all the values, we get:

F1 = (8.99 x 10^9 Nm^2/C^2)(3 x 10^-6 C)(4.5 x 10^-6 C)/(s√2)^2 = 2.55 x 10^-3 N
F2 = (8.99 x 10^9 Nm^2/C^2)(3 x 10^-6