A uniform magnetic field of intensity `1T` is applied in a circular region of radius `0.1 m`, directed into the plane of paper. A charged particle of mass `5xx10^(-5)kg` and charge `q=5xx10^(-4)C` enters the field with velocity `1//sqrt(3)m//s` making an angle of `phi` with a radial line of circular region in such a way that it passes through centre of applied field the angle `phi` is

Options

A. `60^(@)`
B. `30^(@)`
C. `45^(@)`
D. `90^(@)`

Explanation

To solve the problem, we need to find the angle \( \phi \) at which a charged particle enters a uniform magnetic field and passes through the center of the field. Here are the steps to arrive at the solution:

### Step 1: Understand the Problem
We have a charged particle with mass \( m = 5 \times 10^{-5} \, \text{kg} \) and charge \( q = 5 \times 10^{-4} \, \text{C} \) entering a magnetic field of intensity \( B = 1 \, \text{T} \) with a velocity \( v = \frac{1}{\sqrt{3}} \, \text{m/s} \). The particle makes an angle \( \phi \) with the radial line of the circular region of radius \( R = 0.1 \, \text{m} \).

### Step 2: Calculate the Radius of the Path
The magnetic force acting on the charged particle provides the centripetal force required for circular motion. We can equate the magnetic force to the centripetal force:

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