4-space Curl in Vector Calculus - Gauge-institute.org
4-space Curl in Vector Calculus - Gauge-institute.org
4-space Curl in Vector Calculus - Gauge-institute.org
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<strong>Gauge</strong> Institute Journal, Volume 9, No. 3, August 2013<br />
H. Vic Dannon<br />
3.<br />
The Magnetic Induction Forces<br />
the Electron to Spiral towards<br />
the Center<br />
The Lorentz Force on the electron is<br />
<br />
2 2<br />
aB<br />
aB<br />
qv<br />
e e1θ × <br />
1<br />
2<br />
b z = qv<br />
e e<br />
1 <br />
b r,<br />
where ve<br />
is the electron speed, and qe<br />
is the electron charge.<br />
S<strong>in</strong>ce ve<br />
= ωe b , where ωe<br />
is the angular speed, the Lorentz<br />
Force on the electron is<br />
2<br />
<br />
q ω<br />
aB1<br />
.<br />
e e b r<br />
S<strong>in</strong>ce the electron charge<br />
q e<br />
is negative, the force is<br />
aB<br />
( −q<br />
) ω ( −1<br />
).<br />
2<br />
e e b r<br />
<br />
The force direction is opposite to 1 . That is, the force<br />
pushes the electron towards the center, and <strong>in</strong>creases as the<br />
electron gets closer to the solenoid<br />
r<br />
12
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