A beam of protons moving with a velocity 1.6 | vedclass

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(A) The pitch of a helical path is given by the formula $p = v \cos(	heta) 	imes T$,where $T$ is the time period of revolution.The time period $T$ i

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$1.6 	imes 10^{-2} \ m$

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(A) The pitch of a helical path is given by the formula $p = v \cos(	heta) 	imes T$,where $T$ is the time period of revolution.The time period $T$ is given by $T = \frac{2\pi m}{qB}$.Substituting the values: $m = 1.6 	imes 10^{-27} \ kg$,$q = 1.6 	imes 10^{-19} \ C$,$v = 1.6 	imes 10^5 \ m/s$,$B = \frac{\pi}{10} \ T$,and $	heta = 60^{\circ}$.$T = \frac{2 	imes \pi 	imes 1.6 	imes 10^{-27}}{1.6 	imes 10^{-19} 	imes (\pi / 10)} = \frac{2 	imes 10^{-27}}{10^{-19} 	imes 0.1} = 2 	imes 10^{-7} \ s$.Now,the pitch $p = v \cos(60^{\circ}) 	imes T = (1.6 	imes 10^5) 	imes (0.5) 	imes (2 	imes 10^{-7}) = 1.6 	imes 10^{-2} \ m$.

$A$ beam of protons moving with a velocity $1.6 \times 10^5 \ m/s$ enters a uniform magnetic field of $\frac{\pi}{10} \ T$ at an angle $60^{\circ}$ to the direction of the field. The pitch of the helical path of the protons is (mass of proton $= 1.6 \times 10^{-27} \ kg$)

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