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(B) When a charged particle enters a uniform magnetic field perpendicular to its velocity,it follows a semi-circular path of radius $R = \frac{mv}{qB}

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$(B)$ and $(D)$

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(B) When a charged particle enters a uniform magnetic field perpendicular to its velocity,it follows a semi-circular path of radius $R = \frac{mv}{qB}$.Since the magnetic field is semi-infinite,the particles will complete a semi-circle and exit the field region,so $(A)$ is false.Because the particles enter with the same velocity $v$ and the magnetic field $B$ is uniform,they will exit the field moving in the opposite direction to their entry,but still parallel to each other. Thus,$(B)$ is true.The time taken to complete a semi-circle is $t = \frac{\pi m}{qB}$.Since the mass of a proton $(m_p)$ is much greater than the mass of an electron $(m_e)$,the time taken for the proton to exit will be much greater than the time taken for the electron to exit. Thus,$(D)$ is true and $(C)$ is false.Therefore,statements $(B)$ and $(D)$ are correct.

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