A particle of mass m and positive charge q, moving with a uniform velocity v, enters a magnetic field B as shown in (a) Find The radius of the circular arc it describes in the magnetic field. (b) find the angle subtended by the arc at the center. (c ) How long does the particle stay inside the magnetic field? (d) Solve the three parts of the above problem if the charge q on the particle is negative.

Explanation

(a) Radius of circular are , r = mu/ qB `
(b ) since A is tangent to are ABC , Angle described by the particle ,
` /_MAD = 90^@ `
`Now /_NAC = 90^@ `
`OAC = OCA = q ` ,
[by gaometrical principal ]
Then AOC = 180 - (sin theta + thita)`
` = pi - 2 sin theta`
(c ) Distance covered ,brgt ` i = r sin theta = r(pi - 2 sin theta)`
`l= (m)/(qB) ( pi - 2 sin thetab)`
(d) If the charge 'q' of the particule is negtive , then
(1) Redius of circular are `= mu/ qB`
(2) In such a case the center of the are will lie within the magnatic field , bence the angle sulitended by the maasure are
`= pi + 2 sin theta`
(3) Similary the time teken by the
particle to cover the path `= (m)/(qB) (pi + sin theta )` .