- #31
Vibhor
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Option B) 
Charged particle in Electric and Magnetic field
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SUMMARY
The discussion focuses on the motion of a charged particle in a uniform electric field (-E î) and magnetic field (-B î). The particle, projected with an initial velocity of v1 î + v2 j, will return to the origin if the condition given by option B, ##\frac{v_2B}{\pi E}## being an integer, is satisfied. The participants derive the Lorentz force equation, analyze the motion components, and conclude that the particle's trajectory involves circular motion in the x-z plane combined with vertical projectile motion in the y-direction. The final coordinates of the particle are expressed as ##x=\frac{v_1m}{qB}sin(ωt)##, ##y = v_2t - \frac{qE}{2m}t^2##, and ##z = -\frac{v_1m}{qB}(1-cos(ωt))##.
PREREQUISITES- Understanding of Lorentz force: ##\vec{F} = q\vec{v} \times \vec{B} + q\vec{E}##
- Familiarity with circular motion and projectile motion concepts
- Basic knowledge of differential equations and their solutions
- Ability to manipulate trigonometric functions and understand angular frequency (ω)
- Study the derivation and applications of the Lorentz force in electromagnetic fields
- Learn about the conditions for periodic motion in charged particle dynamics
- Explore the solutions to systems of differential equations in physics
- Investigate the relationship between electric and magnetic fields in particle motion
Students and educators in physics, particularly those focusing on electromagnetism and classical mechanics, as well as researchers analyzing charged particle dynamics in electric and magnetic fields.
- #32
ehild
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CorrectVibhor said:Option B)
. Was it difficult?- #33
Vibhor
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ehild said:
It surely was until you took over
. Honestly speaking , I had almost made up my mind to leave this problem as I was completely clueless 
. But last couple of hours of problem solving were pretty exciting 
,thanks to you .You are amazing
.- #34
ehild
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It was the combination of a circular motion in the x,z plane and a vertical projectile motion in the direction of y. The period of the circular motion should be the same as the flight time of the vertical projectile.
Thank you for the thanks
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