Sum

In a cyclotron, magnetic field of 3·5Wb/m2 is used to accelerate protons. What should be the time interval in which the electric field between the Dees be reversed?

(Mass of proton = 1· 67 x 10^{-27}Kg, Charge on proton =1·6x10^{-19}c).

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#### Solution

B = 3.5 Wb/m^{2} , m_{P} = 1.67 × 10^{-27} Kg,

e = 1.6 × 10^{-19} C,

t = ?

t = `pi"m"_"P"/"Bq"_"p"`

t = `(3.142 xx 1.67 xx 10^-27)/(3.5 xx 1.6 xx 10^-19)`

`= (3.142 xx 1.67)/(3.5 xx 1.6) xx 10^-8`

= [log (3.142) + log (1.67) - log (3.5) - log (1.6)] × 10^{-8}

= [0.4972 + 0.2227 - 0.5441 - 0.2041] × 10^{-8}

= [antilog (- 0.0283)] × 10^{-8} s

= 0.9369 × 10^{-8} s

= 9.369 × 10^{-9} s

The dees should be reversed within time interval of 9.369 × 10^{-9} S.

Concept: Motion in Combined Electric and Magnetic Fields - Cyclotron

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