Coulomb's Law Problem and charged particles

[bbbbbev]

I cannot figure out this problem. I mean, I can't really even figure out what it is asking. I am not expecting anyone to solve it for me or anything. I just need some help as to how to get started.

Particles A and B Figure 22-25a shows charged particles A and B that are fixed in place on an x axis. Particle A has an amount of charge of |qA| = 9.00e. Particle C, with a charge of qC = +9.00e, is initially on the x-axis near particle B. Then particle C is gradually moved in the positive direction of the x axis. As a result, the magnitude of the net electrostatic force net, B on particle B due to particles A and C changes. Figure 22-25b gives the x-component of that net force as a function of the position x of particle C. The plot has an asymptote of net, B = 1.553 10-25 N as x . As a multiple of e, what is the charge qB of particle B?

Figure 22-25a is basically a plot of three points, with point (a) on the negative x axis, point (b) at the origin, and point (c) on the positive x axis. Then there is also a graph of Fnet-->b. I don't know if you can figure out the problem without the graph, but any help on how to do it would be greatly appreciated!

Thanks,
Beverly

 

[Andrew Mason]

I cannot figure out this problem. I mean, I can't really even figure out what it is asking. I am not expecting anyone to solve it for me or anything. I just need some help as to how to get started.

Try writing out the Coulomb force of C on B and A on B. The vector sum of those two forces will be the net force. F should be a function in the form:

$$F = kq_b(q_a/A^2 + q_c/x^2)$$

Now the first issue is: is q_a negative or positive? Then determine if q_b is positive or negative.

I can't figure out from your information what the graph looks like. You should be able to figure the kind of charge for q_a and q_b from just looking at the direction of F(x). If the F(x)<0 as x approaches 0 then q_b would be negative. If it is greater than 0, q_b would be positive.

I can't tell from your description what the equation of the asymptote is. Can you provide it?

AM

 

[wais]

Hi Beverly,

Thank you for reaching out for help with this Coulomb's Law problem. It can definitely be confusing and overwhelming at first, but with some guidance, I'm sure you'll be able to figure it out.

First, let's break down the problem and try to understand what it is asking. We are given three particles on an x-axis - A, B, and C. Particle A has a charge of 9.00e (where e represents the elementary charge), particle B has an unknown charge qB, and particle C has a charge of +9.00e. Particle A and B are fixed in place, while particle C is initially positioned near particle B and then moved gradually in the positive direction of the x-axis.

We are then given a graph in Figure 22-25b that shows the x-component of the net electrostatic force on particle B due to particles A and C. The graph shows that as particle C is moved closer to particle B, the net force on particle B increases. However, as particle C moves further away from particle B, the net force on particle B decreases and approaches an asymptote (a value that the function approaches but never reaches) of 1.553 x 10^-25 N. Essentially, the graph is showing us the relationship between the distance of particle C from particle B and the net force on particle B.

Now, the question is asking us to find the charge of particle B, qB, in terms of e. This means we need to express qB as a multiple of the elementary charge e. To do this, we can use Coulomb's Law, which states that the force between two charged particles 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 * (q1 * q2) / r^2

where F is the force, k is the Coulomb's constant (a proportionality constant), q1 and q2 are the charges of the particles, and r is the distance between them.

In our problem, we can use this equation to find the relationship between the distance of particle C from particle B and the net force on particle B. Since we know the charges of particles A and C, we can plug them into the equation, along with the distance between them (which is also the distance between particle C and B), and solve for the force