A dipole with a positive charge at
x=0.0 nm, y=10.0 nm and a negative charge at x=0.0 nm, y = -10.0 nm. If the charge have a value equivalent to that of a proton and an electron,respectively, what is the dipole moment?
3.2 x 10^-27 C*m
Well, it seems like these charges are having a "positive" and "negative" relationship in terms of their location. It's like they're poles apart! Pun intended.
Now, to calculate the dipole moment, we need to find the product of the magnitude of either charge and the distance between them. Since we're dealing with a proton and an electron, let's consider the magnitude of charge for an electron (I don't want to play favorites, but electrons are smaller, so they need a little boost).
The magnitude of charge for an electron is approximately 1.6 x 10^-19 C. So we have q1 = 1.6 x 10^-19 C and q2 = -1.6 x 10^-19 C.
Now, the distance between them is the difference in their y-coordinates: 10.0 nm - (-10.0 nm), which simplifies to 20.0 nm.
Thus, the dipole moment (p) is given by the formula p = q * d, where q is the magnitude of charge and d is the distance between the charges.
Substituting the values we have, we get p = (1.6 x 10^-19 C) * (20.0 x 10^-9 m).
Simplifying this, p = 32 x 10^-28 C·m.
So, the dipole moment is approximately 32 x 10^-28 C·m.
To calculate the dipole moment of a system, we first need to understand what the dipole moment represents. The dipole moment is a measure of the separation and magnitude of the positive and negative charges within a system.
The dipole moment (μ) is given by the product of charge (q) and the displacement vector (d) between the positive and negative charges:
μ = q * d
In this case, we have a positive charge equivalent to that of a proton (q1 = +e) and a negative charge equivalent to that of an electron (q2 = -e), where e is the elementary charge. The displacement vector in the y-direction is given as 20.0 nm.
To find the dipole moment, we can first calculate the magnitude of the dipole moment (|μ|), and then determine its direction.
1. Calculate the magnitude of the dipole moment:
We know that the magnitude of the dipole moment is given by:
|μ| = |q1 * d|
Since the x-coordinate of both charges is the same (x = 0.0 nm), the only difference in coordinate is in the y-direction, so we can calculate the magnitude of the dipole moment as:
|μ| = |q1 * (y2 - y1)|
Substituting the values, let's calculate the magnitude of the dipole moment:
|μ| = |(+e) * (10.0 nm - (-10.0 nm))|
2. Determine the direction of the dipole moment:
The dipole moment points from the negative charge to the positive charge.
Therefore, the direction of the dipole moment is in the negative y-direction.
Putting it all together, the dipole moment (μ) is given by the magnitude (|μ|) and the direction:
μ = -|μ| ŷ,
where ŷ is the unit vector in the negative y-direction.
Now, you can substitute the values and calculate the dipole moment.