Couloumb's Law 3 charges on a line

[PatrickGeddes]

I did this problem just the way I took notes on it in class and keep coming up with the wrong answer. Please help I've spent nearly 2 hours on this one simple problem. Thanks.
Problem: Three point charges lie along a straight line as shown in the figure below, where q1 = 6.36 µC, q2 = 1.56 µC, and q3 = -1.84 µC. The separation distances are d1 = 3.00 cm and d2 = 2.00 cm. Calculate the magnitude and direction of the net electric force on each of the charges.

 

[tms]

You have to show your work so far.

 

[PatrickGeddes]

Ok sorry, first time using the site. I did F of q1 on q2 is ((8.99x10^9) x .00000636 C x .00000156 C)/.0009 m=99.10576 N and F of q3 on q2 is ((8.99x10^9) x -.00000184 C x .00000156 C)/.0016 m=-286.72 N. Then for the Force on the middle charge I just added them together to get -187.8 N.

 

[PatrickGeddes]

Is this enough work so far?

 

[asteriatic]

First of all, don't get discouraged! Coulomb's Law can be tricky, but with some practice and understanding of the concepts, you will be able to solve these types of problems easily.

To solve this problem, we will use Coulomb's Law, which states that the magnitude of the electric force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. Mathematically, it can be written as F = k(q1q2)/r^2, where k is the Coulomb's constant (9x10^9 Nm^2/C^2), q1 and q2 are the charges, and r is the distance between them.

Now, let's begin by finding the net electric force on q1. We will consider the forces from q2 and q3 separately and then add them together.

From q2, the distance is d1 = 3.00 cm = 0.030 m. Plugging in the values, we get F1 = k(q1q2)/d1^2 = (9x10^9)(6.36x10^-6)(1.56x10^-6)/(0.030)^2 = 1.68x10^-5 N.

Note that this force is directed towards the right, as q1 and q2 have opposite charges and therefore attract each other.

From q3, the distance is d2 = 2.00 cm = 0.020 m. Plugging in the values, we get F2 = k(q1q3)/d2^2 = (9x10^9)(6.36x10^-6)(-1.84x10^-6)/(0.020)^2 = -3.39x10^-5 N.

Note that this force is directed towards the left, as q1 and q3 have like charges and therefore repel each other.

Now, to find the net force on q1, we simply add these two forces together: Fnet = F1 + F2 = 1.68x10^-5 - 3.39x10^-5 = -1.71x10^-5 N. This means that the net force on q1 is directed towards the left with a magnitude of 1.71x10^-5 N.

Similarly, we can find the net force on q2 and q3