Problem 2: Bhelpuri Problem

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Problem Statement:

(‘Bhelpuri’ refers to a street food dish made by mixing different varieties of ingredients)

A setup of thin metal pieces is constructed in a fashion similar to the function

 where [.] is GIF (Greatest Integer Function)  ……(1)

Consider only the region 0<= x <=4p, and there are large conducting plates of area ‘A’ placed at x = 5p (plate 2) and x = -p (plate 1). Given that,  A>> 6p.

Now, a small conducting ball with charge ‘+q’ and mass ‘m’ is thrown with a velocity towards the y=p graph in (1) as shown below.

Bhelpuri Problem Figure 1: A ball approaches the plate with a velocity making an angle theta with the horizontal
Figure 1: A ball approaching the plate

The collision between the metal step and the ball is perfectly inelastic in nature. The ball and the metal step are connected to a circuit as shown below :

Bhelpuri Problem Figure 2: The figure shows the complete circuit schematic
Figure 2: Circuit Schematic

(The above figure is just the electric circuit, which shows how things are connected; it doesn’t give the representation of the actual setup.) For actual setup, refer question.

Question: 

If this is the case, then what should be the magnitude of the electric field required to make the ball just cross the lower metal step (i.e., y=0)? 
(Assume no friction anywhere and consider that the metal steps don’t affect the electric field between the plates)

Solution has been uploaded. You can access the solution by clicking the button below.

Solution to Bhelpuri Problem (Click Here)

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