Particle Motion in Uniform Electric and Magnetic Fields

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A particle with charge q and mass m is projected on a rough horizontal plane under the influence of uniform electric and magnetic fields. It experiences a spiral motion due to these fields, along with gravitational acceleration and friction. The discussion revolves around determining the time taken for the particle to reach the origin from its initial position. The original poster initially sought help but later resolved the problem independently. The interaction highlights the complexities of particle motion in combined electric and magnetic fields.
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Homework Statement


A particle of charge q and mass m is projected on a rough horizontal plane (X-Y) from a point (a,0,0) with initial velocity v = V j . In space there exists uniform electric and magnetic field E k and -B k respectively. Acceleration due to gravity is g and friction coefficient between particle and plane is u . The particle moves on a spiral path and finally reaches origin O. The time taken to reach the origin = ?

Homework Equations

The Attempt at a Solution

 
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Tachyon_Jay said:

The Attempt at a Solution

Have you attempted the problem? Please show your attempt to get help.
 
Never Mind. I solved it. Thanks.
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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