Uniform electrilcf and magnetic fields with strength E and B are directed along of x-axis. A particle with specific charge `q/m` leves the origin in the direction of x-axis with an initial velocity `v_0`. Find a. the y-coordinate of the particle when it crosses the y-xis for nth time. b. the angle `alpha` between the particle's velocity vector adn the y-axis for nth time
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To solve the problem, we will break it down into two parts as per the question:
### Part (a): Finding the y-coordinate of the particle when it crosses the y-axis for the nth time.
1. **Understanding the Motion**: The particle moves in a helical path due to the presence of uniform electric (E) and magnetic (B) fields. The helical path's axis is parallel to the y-axis.
2. **Time to Cross the Y-axis**: The time taken for the particle to cross the y-axis for the nth time can be expressed as:
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