How Does a Magnetic Field Affect Liquid Levels in a U-Tube?

[gaobo9109]

Homework Statement

A u-tube of uniform square cross section has electrodes sealed inside the upper and lower walls of the horizontal section. The two arms of tube being vertical. The tube is partially filled with liquid sodium and a direct current is passed between the electrodes. A uniform horizontal magnetic flux is also applied to the horizontal section of the tube in a direction normal to the vertical plane containing the tube

The level of the liquid in the two vertical arms changes on application of the field.
Cross sectional area of the tube = A
Current between the electrode = I
Density of the liquid sodium = P

Given that a magnetic flux density of B is applied, by how much will the liquid level in one arm differs from the liquid level in the other arm?

Homework Equations

F = IBL

The Attempt at a Solution

I am guessing it has something to do with pressure at the point magnetic field is applied and the atmospheric pressure

 

[AvroArrow]

. Let h1 and h2 be the heights of liquid levels in the two arms. Force acting on the liquid due to the magnetic field = IBLAHence, pressure difference between the two arms = IBLA/A = IBL Atmospheric pressure = Pgh1 and Pgh2 So, Pressure difference between the two arms = Pgh2 - Pgh1 Therefore, IBL = Pgh2 - Pgh1 Hence, h2 - h1 = IBL/Pg Therefore, the difference between the liquid levels in the two arms is (IBL/Pg).