An electron and a proton of equal linear momentum enter in a direction perpendicular to a uniform magnetic field. If the radii of their circular paths are rₑ and rₚ respectively, then (rₑ)/(rₚ) is equal to . (mₑ= mass of the electron, mₚ= mass of the proton)

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(2) 1. Given: an electron and a proton with the same linear momentum p, each entering perpendicular to the same field B. Idea: the magnetic force supplies the centripetal force, qvB=(mv²)/r, so r=(mv)/(qB)=p/(qB). Written this way the radius depends only on the momentum, the charge and the field — not on the mass separately. The electron and the proton carry charge of the same magnitude e, and p and B are the same for both. So rₑ=p/(eB)=rₚ and the ratio is 1.

An electron and a proton of equal linear momentum enter in a direction perpendicular to a uniform magnetic field. If the radii of their circular paths are rₑ and rₚ respectively, then (rₑ)/(rₚ) is equal to ______. (mₑ= mass of the electron, mₚ= mass of the proton)

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