An electron and a proton having equal momentum enter in a uniform magnetic field normal to the lines of force. If the radii of curvature of circular paths be re and rp respectively, then :
Question
An electron and a proton having equal momentum enter in a uniform magnetic field normal to the lines of force. If the radii of curvature of circular paths be re and rp respectively, then :
Solution
The radii of curvature of the circular paths for the electron and proton can be determined by the formula:
r = mv/qB
where:
- r is the radius of curvature,
- m is the mass of the particle,
- v is the velocity of the particle,
- q is the charge of the particle, and
- B is the magnetic field strength.
Given that the electron and proton have equal momentum, we can say that:
me * ve = mp * vp
where:
- me and mp are the masses of the electron and proton respectively, and
- ve and vp are the velocities of the electron and proton respectively.
From this, we can derive that:
ve/vp = mp/me
Substituting this into the formula for the radius of curvature, we get:
re/rp = me/mp
Therefore, the ratio of the radii of curvature of the electron and proton is equal to the ratio of their masses.
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