Question

Consider the situation of the previous problem. A particle having charge q and mass m is projected from the point Q in a direction going into the plane of the diagram. It is found to describe a circle of radius r between the two plates. Find the speed of the charged particle.

Answer 1

The speed of the charged particle is given by $\frac{\mu_{0} k q r}{m}$

Explanation:

According to question,

Charge = q  

Mass = m  

Radius = r  

We know the radius in a magnetic field defined by a charged particle is given by

$r=\frac{m v}{q B}$

Ampere circuital law:- The Circuital Law of Ampere notes the relation it provides between the magnetic field. This law says integral density of the magnetic field (B) along the imaginary closed path is the same as the current product including the High Path and Durability.

Using Ampere circuital law

$\int B \cdot d l=\mu_{0} i$

$B . d l=\mu_{0} k d l$

$B=\mu_{0} k$

$v=\frac{B q r}{m}$

 $=\frac{\mu_{O} k q r}{m}$

Answer 2

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Please refer the above attachment