Force on a polarized molecule due to a charged wire

[Shaybay92]

Homework Statement

A polarized water molecule is near a long charged wire and experiences a force due to the charge. How do you determine the net force on this molecule assuming the molecule is perpendicular to the center of the rod and nothing polarizes further.

The Attempt at a Solution

I just treated each end of the molecule as a point charge and added up the forces Fnet on the whole molecule from the rod using F = EQ. Is this correct? I was supposed to get an answer that didnt involve the separation or polarizability but I always got stuck with separation 's'.

 

[mark726]

I would approach this problem by first understanding the concept of polarization and its effects on a water molecule near a charged wire. I would also review the equations and principles related to electric forces and fields.

Based on my knowledge, I would determine the net force on the polarized water molecule using the following steps:

1. Identify the direction of the electric field created by the charged wire. This can be done by using the right hand rule, where the thumb points in the direction of the current flow and the fingers curl in the direction of the magnetic field.

2. Determine the direction of the dipole moment of the water molecule. This can be done by considering the partial charges on the molecule and their relative positions.

3. Calculate the magnitude of the electric field at the position of the water molecule using the equation E = kQ/r^2, where k is the Coulomb's constant, Q is the charge on the wire, and r is the distance between the wire and the molecule.

4. Calculate the torque experienced by the water molecule using the equation τ = pEsinθ, where p is the dipole moment of the molecule, E is the electric field, and θ is the angle between the dipole moment and the electric field.

5. Use the equation F = τ/l, where l is the length of the molecule, to find the net force on the molecule. This assumes that the molecule is perpendicular to the charged wire.

By following these steps, I can determine the net force on the polarized water molecule without involving the separation or polarizability. However, if the separation or polarizability of the molecule is known, these can be incorporated into the calculations to get a more accurate result.