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Purpose 1.To study the effect of electric and magnetic fields on charged particles and to measure the charge to mass ratio of an electron.(1/2) m v2 = e V (3) Combining equations (2) and (3) gives e / m = ( 2 V / B2 r2) (4) Thus, when the accelerating voltage V, the magnetic field B, and the radius of the circular path r are known, the value of the e/m ratio can be computed and is given in units of C/kg by equation (4) if V is in volts, B in Teslas and r in meters.Theory When an electron moves in a magnetic field B whose direction is perpendicular to the velocity v of the particle, it is acted on by a force F perpendicular to B and v with a magnitude given by: |The force F is equal to the mass of the particle times the centripetal acceleration e v B = m v2 / r (2) where r is the radius of the circle and m is the mass of the electron.More practice in error analysis.2.F |
Original text
Purpose
- To study the effect of electric and magnetic fields on charged particles and to
measure the charge to mass ratio of an electron. - More practice in error analysis.
Theory
When an electron moves in a magnetic field B whose direction is perpendicular to
the velocity v of the particle, it is acted on by a force F perpendicular to B and v with
a magnitude given by:
| F | = e v B (1)
where e is magnitude of the charge of the electron. This force causes the particle to
move in a circle in the plane perpendicular to the field. The force F is equal to the
mass of the particle times the centripetal acceleration
e v B = m v2 / r (2)
where r is the radius of the circle and m is the mass of the electron. If the electron
has been accelerated from rest through a potential difference V, then the kinetic
energy is equal to the loss of potential energy.
(1/2) m v2 = e V (3)
Combining equations (2) and (3) gives
e / m = ( 2 V / B2 r2) (4)
Thus, when the accelerating voltage V, the magnetic field B, and the radius of the
circular path r are known, the value of the e/m ratio can be computed and is given in
units of C/kg by equation (4) if V is in volts, B in Teslas and r in meters.
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