A uniform magnetic field is applied in a circular region of radius R as shown in the given figure. A charged particle of charge q and mass m enters with a velocity from point P along the line that is making an angle with the line segment OP, in the region of magnetic field.

The charged particle is found to pass through the centre of the circular region. Find the angle `theta`.
Given : `B = 1 T, R = 10 cm, m = 6 xx 10^(-3) kg , q = 6 xx 10^(-2) C, v = 1 //sqrt3`.

Explanation

from the figure it can be easily understood that the locus of the charged particle is symmetric about point Q .
Radius of the path followed by the particle can be written as follows:
`r = (mv)/(qB) = (6 xx 10^(-3) xx 1 //sqrt3)/(6 xx 10^(-2) xx 1) = 1/(10sqrt3) m`
Refer the figure again to understand the following:
`cos theta = (R//2)/r = ((0.1))/2 10 sqrt3 = sqrt3/2`
Here , ` theta = 30^(@)`.