An electron and a proton have equal kinetic e | vedclass

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(D) When a charged particle enters a magnetic field perpendicularly,it follows a circular path.The radius of the circular path is given by $r = \frac{

Vedclass · Accepted Answer

All the statements are false.

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(D) When a charged particle enters a magnetic field perpendicularly,it follows a circular path.The radius of the circular path is given by $r = \frac{mv}{qB}$.Since kinetic energy $K = \frac{1}{2}mv^2$,we have $mv = \sqrt{2mK}$.Substituting this into the radius formula,we get $r = \frac{\sqrt{2mK}}{qB}$.Since the electron and proton have the same kinetic energy $(K)$ and enter the same magnetic field $(B)$,the radius $r$ depends on $\frac{\sqrt{m}}{q}$.Because the mass of a proton $(m_p)$ is much larger than the mass of an electron $(m_e)$,their radii will be different.Therefore,both follow circular paths,but with different radii. Thus,options $A$,$B$,and $C$ are incorrect,making $D$ the correct statement.

An electron and a proton have equal kinetic energies. They enter a magnetic field perpendicularly. Then:

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