An electron and a proton have equal kinetic energies. They enter in a magnetic field perpendicular to B , then

Question

An electron and a proton have equal kinetic energies. They enter in a magnetic field perpendicular to B , then, Both will follow a circular path with same radius, Both will follow a helical path, Both will follow a parabolic path, All the statements are false

MARKS App · Accepted Answer

For such a motion, magnetic force = centripetal force q v B = m v 2 r ⇒ q B = m v r ⇒ r = m v q B ∴ r p r c = m p v p q B × q B m e v e but K e = K p (given) ⇒ 1 2 m e v e 2 = 1 2 m p v p 2 ⇒ m p m e = v e v p 2 ∴ r p r e = v e v p 2 v p v e = v e v p Hence, the electron and proton will follow circular paths but with different radii.

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