### Problem 2.4: Displacement of a Magnetic Bead on a Kelvin Body**Scenario:**Consider a cell with a magnetic bead attached to it. The cell is treated as a Kelvin body. Initially, a magnetic field is applied for a prolonged period, exerting a constant force \( F_0 \) on the bead. At time \( t = 0 \), this force is abruptly turned off.**Task:**Derive an expression for the displacement of the bead as a function of time, \( x(t) \). Utilize existing formulae as needed without re-deriving them.**Instructions:**- Focus on the dynamics following the removal of the force.- Ensure all steps are logically explained.- Emphasize the mechanical properties of the Kelvin body that influence the bead's displacement over time.**Note:**The exploration should align with known theoretical principles such as viscoelasticity associated with a Kelvin body (also known as a Kelvin-Voigt material), characterized by spring and dashpot elements in a parallel configuration.

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2.4 Consider a cell that has a magnetic bead attached to it. We will treat the cell as a Kelvin body. Suppose that the magnetic field has been turned on for a very long time and is producing a constant force on the bead Fo. At time t=0, the force is suddenly switched off. Derive an expression for the resulting displacement of the bead as a function of time, x(t). Note that you do not need to re-derive any formulae given in the text.

2.4 Consider a cell that has a magnetic bead attached to it. We will treat the cell as a Kelvin body. Suppose that the magnetic field has been turned on for a very long time and is producing a constant force on the bead Fo. At time t=0, the force is suddenly switched off. Derive an expression for the resulting displacement of the bead as a function of time, x(t). Note that you do not need to re-derive any formulae given in the text.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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