Magnitude of the Net Electrostatic Force On an Oxygen Atom

[shimizua]

Homework Statement

The water molecule forms an angle, with hydrogen atoms at the tips and the oxygen atom at the vertex (see diagram in the previous problem).
Assume that the angle at the oxygen atom is Θ = 103.5o and the distance between the oxygen and the hydrogen atoms is d = 93.1 x 10-9 m.
Calculate the magnitude of the net electrostatic force on the oxygen atom. Use the charges from the previous problem.

This next stuff is what i have already figured out in a different problem that they want you to use in this one.
The water molecule consists of two hydrogen atoms and one oxygen atom. Since the oxygen atom has a higher electronegativity than the hydrogen atom, the side of the molecule with the oxygen atom has a partial negative charge. Assume that the partial negative charge on the oxygen atom is Q1 = -1.104 x 10-19 C. What is the magnitude of the charge Q2 on each hydrogen atom?

and here is the picture.
http://jilawww.colorado.edu/beckergroup/figures/Water.jpg
For this part i got an answer of 5.52e-20 C which the computer said was correct.
that should be all the info you need

Homework Equations

so i am pretty sure that you do F=(k*q1*q2)/r^2 but i am just unsure of why they give you the angle of the oxygen to the hydrogen and what to do with it. please help me!

The Attempt at a Solution

well k is a constant that is 9*10^9 (i think) q2 is the 5.52e-20 C that i found inthe other equation, i am trying to find q1 and r 1/2(93.1x10^-9) but other then that i have no idea what to do.

 

[Carid]

Isn't the question asking you for the vector sum of the two electrostatic forces on the oxygen atom due to the two hydrogen atoms?

 

[thomate1]

I would approach this problem by first understanding the concept of electrostatic forces and how they are calculated. The equation F=(k*q1*q2)/r^2 is known as Coulomb's Law and is used to calculate the electrostatic force between two charges, where k is the Coulomb's constant, q1 and q2 are the magnitudes of the charges, and r is the distance between them.

In this problem, we are given the distance between the oxygen and hydrogen atoms (d=93.1 x 10^-9 m) and the magnitude of the partial negative charge on the oxygen atom (Q1 = -1.104 x 10^-19 C). We are also given the angle at the oxygen atom (Θ = 103.5o), which is important because it affects the direction of the electrostatic force.

To calculate the magnitude of the net electrostatic force on the oxygen atom, we need to consider the electrostatic force from each hydrogen atom separately. Since the hydrogen atoms have a positive charge due to the partial negative charge on the oxygen atom, the electrostatic force from each hydrogen atom will be repulsive.

Using Coulomb's Law, we can calculate the magnitude of the electrostatic force from each hydrogen atom on the oxygen atom. The distance between them (r) is equal to half of the distance between the oxygen and hydrogen atoms, since the angle is 103.5o. So, r = 1/2(93.1 x 10^-9 m) = 46.55 x 10^-9 m.

Plugging in the values, we get F1 = (9 x 10^9 N*m^2/C^2)*(-1.104 x 10^-19 C)*(5.52 x 10^-20 C)/(46.55 x 10^-9 m)^2 = -2.69 x 10^-14 N. Since this force is repulsive, the negative sign indicates that it is acting in the opposite direction of the positive charge on the hydrogen atom.

We can repeat this calculation for the second hydrogen atom, and then find the net electrostatic force on the oxygen atom by adding the two forces together. Since the two forces are acting at an angle of 103.5o, we can use vector addition to find the magnitude of the net force, which will be the hypotenuse of a right triangle formed by the two