Calculating Oil Height Between Coaxial Tubes with Dielectric Homework

[SpY]]

Homework Statement

Two coaxial metal tubes (placed vertically) have an inner radius a and outer radius b. They are placed vertically between a dielectric oil (with susceptibility X and mass density p). The inner tube has potential V and the outer one is grounded (V=0). How high will the oil rise in the space between the tubes?

2. Homework Equations (and attempt at solution)

Starting with these equations is my attempt at a solution :P
$$\vec{p} = \epsilon_0 \chi \vec{E}$$
$$h = \epsilon_0 (1 + \chi) \vec{E}<br /> = \epsilon_0 \vec{E} + \vec{p}$$

And the permittivity is
$$\epsilon_0 (1 + \chi)$$
$$h$$ height of displacement
$$\vec{p}$$ electric dipole moment
$$\chi$$ susceptibility
$$\epsilon_0$$ permittivity in free space
$$\vec{E}$$ electric field

 

[gabbagabbahey]

Homework Statement

Two coaxial metal tubes (placed vertically) have an inner radius a and outer radius b. They are placed vertically between a dielectric oil (with susceptibility X and mass density p). The inner tube has potential V and the outer one is grounded (V=0). How high will the oil rise in the space between the tubes?

2. Homework Equations (and attempt at solution)

Starting with these equations is my attempt at a solution :P
$$\vec{p} = \epsilon_0 \chi \vec{E}$$
$$h = \epsilon_0 (1 + \chi) \vec{E}<br /> = \epsilon_0 \vec{E} + \vec{p}$$

And the permittivity is
$$\epsilon_0 (1 + \chi)$$
$$h$$ height of displacement
$$\vec{p}$$ electric dipole moment
$$\chi$$ susceptibility
$$\epsilon_0$$ permittivity in free space
$$\vec{E}$$ electric field

This looks more like a random guess than an attempt at a solution. Dipole moment and height don't even have the same units, so, without even working out the solution, I can tell you your guess is wrong.

Instead of randomly mashing formulas together, try applying some physical laws. In order for the oil to rise (it must change its momentum to do so), what must be exerted on it (hint: it rhymes with a "met horse" )? What forces are acting on the oil? What is the rate of change of the oil's momentum when it reaches its new maximum height? What does that tell you about the net force on it?