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Find the average force on the loop
[From: ] [author: ] [Date: 11-11-24] [Hit: ]
the question implicitly assumes a direction of rotation for the electron. Using Fleming’s LH rule, it’s a bit awkward but:First finger = field; points radially outwards.Thumb gives = direction of force (along +z).Second finger = current; points in the opposite direction to electron flow (as electrons are negative).I think this gives clockwise for the electron direction,......
Since
(tangential) and the effective (radially outwards) are always perpendicular, the average (constant magnitude) force acts along .
(In fact it could be or <-k> but the question has assumed a direction of rotation which makes the force along .)
= e |v|
= [aB/√(a² + h²)] e [√ [2/m)(E + e²/(4πεa))]
= aeB√ [2/(m(a² + h²)][E + e²/(4πεa)]]
This is the expression we are asked to prove.
As noted above, the question implicitly assumes a direction of rotation for the electron. Using Fleming’s LH rule, it’s a bit awkward but:
First finger = field; points radially outwards.
Thumb gives = direction of force (along +z).
Second finger = current; points in the opposite direction to electron flow (as electrons are negative).
I think this gives clockwise for the electron direction, when viewed from the origin – but it’s quite awkward – I could be wrong!
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I guess I stumbled on the math.
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