Explain with the help of a well labelled diagram.
During an experiment with magnetism, a scientist is able to create a uniform magnetic field of 0.1T. He then projects a bunch of protons into this field at an angle of 90. The straight line motion path of the protons gets deviated. Find this deviation after the protons have traversed a distance of 1 cm.  Take velocity =10000 km/s, mass of proton = 1.65 × 10^25kg.

Dear Student,

Please find below the solution to the asked query:

Mass of the proton value is given wrong. I am considering the actual value of the proton mass.

The radius of the circular path followed by the charged particle is,

$$\begin{gathered} r=\frac{mv}{qB}=\frac{1.67\times {10}^{-27}\times {10}^7}{1.6\times {10}^{-19}\times 0.1}=1.04 cm \\ So, the path will be deviated by an angle, \\ d=r \sin \theta \Rightarrow \sin \theta =\frac{d}{r}\Rightarrow sin \theta =\frac{1}{1.04}=0.958 \\ \Rightarrow \theta ={\sin }^{-1}\left\{0.958\right\}=1.28 rad=1.28\times \frac{180}{3.14} \\ \Rightarrow \theta =73.{38}^0 \end{gathered}$$

The path will be as in the below diagram.

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