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A hydrogen ion of mass m and charge q tr...

A hydrogen ion of mass m and charge q travels with a speed v along a circle of radius r in a uniform magnetic field of flux density B. Obtain the expression for the magnetic force on the ion and determine its time period.

Text Solution

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As hydrogen ion is describing a circular path in a uniform magnetic field, hence force on hydrogen ion due to perpendicular magetic field is providing the centripetal force. So
`Bqvsin90^@=(mv^2)/(r)` or `r=(mv)/(qB)`
Time period of revolution of hydrogen ion
`T=(2pir)/(v)=(2pi)/(v)xx(mv)/(qB)=(2pim)/(qB)`
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