The dipole moment of the water molecule (H2 O) is 6.17 ×10^-36 C ·m . Consider a water molecule

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The dipole moment of the water molecule (H2 O) is 6.17...

The dipole moment of the water molecule $\left(\mathrm{H}_{2} \mathrm{O}\right)$ is $6.17 \times 10^{-36} \mathrm{C} \cdot \mathrm{m} .$ Consider a water molecule located at the origin whose dipole moment $\vec{p}$ points in the $+x$ -direction. A chlorine ion $\left(\mathrm{Cl}^{-}\right),$ of charge $-1.60 \times 10^{-19} \mathrm{C},$ is located at $x=3.00 \times 10^{-9} \mathrm{~m}$ Find the magnitude and direction of the electric force that the water molecule exerts on the chlorine ion. Is this force attractive or repulsive? Assume that $x$ is much larger than the separation $d$ between the charges in the dipole, so that the approximate expression for the electric field along the dipole axis derived in Example 21.14 can be used.

The dipole moment of the water molecule $\left(\mathrm{H}_{2} \mathrm{O}\right)$ is $6.17 \times 10^{-36} \mathrm{C} \cdot \mathrm{m} .$ Consider a water molecule located at the origin whose dipole moment $\vec{p}$ points in the $+x$ -direction. A chlorine ion $\left(\mathrm{Cl}^{-}\right),$ of charge $-1.60 \times 10^{-19} \mathrm{C},$ is located at $x=3.00 \times 10^{-9} \mathrm{~m}$
Find the magnitude and direction of the electric force that the water molecule exerts on the chlorine ion. Is this force attractive or repulsive? Assume that $x$ is much larger than the separation $d$ between the charges in the dipole, so that the approximate expression for the electric field along the dipole axis derived in Example 21.14 can be used.

Key Concepts

Dipole Approximation

The dipole approximation is used when the distance from the dipole to the point of interest is much larger than the separation between the dipole's charges. This allows the electric field to be expressed in a simplified form, typically showing an inverse-cube dependence on distance, which simplifies the analysis of the dipole's effect on external charges.

Force on a Charge in an Electric Field

When a charged particle is placed in an electric field, it experiences a force calculated as the product of its charge and the field at its location. This principle, expressed as F = qE, is fundamental for determining the interactions between charges and electric fields in various physical situations.

Electric Field of a Dipole

The electric field produced by a dipole, especially in regions far from the dipole (where the separation between charges is much smaller than the distance to the observation point), decreases with the cube of the distance. Along the axis of the dipole, this field is aligned with the dipole moment and is used to approximate the influence of the dipole on nearby charges.

Dipole Moment

The dipole moment is a vector quantity that quantifies the strength and orientation of a dipole, defined as the product of the magnitude of one of the charges and the distance separating the charges. This moment is central to understanding how molecules, such as water, interact with electric fields.

Electric Dipole

An electric dipole consists of two equal and opposite charges separated by a finite distance. It is a basic concept in electromagnetism used to describe systems that have a separation of positive and negative charges, which creates a distinct directional behavior in the resulting electric field.

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