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Mr Virtual
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Homework Statement
I hope I am not posting this question at the wrong place, but can someone explain to me the vector product rule, or cross product rule. I don't seem to get the hang of it.
Why I am asking this is because I want to know how force on a moving charge due to an applied B-field works, how it works in the direction perpendicular to B and v.
Homework Equations
If A and B are two vectors, then
A X B = ABsin theta
the direction of the resultant is perpendcular to the plane in which the two vectors A and B lie.
For magnetic field,
F=q (B x v)
q=charge
B=applied magnetic field
v=vel of charge
The Attempt at a Solution
We are taught the cross product rule with the help of screw-wrench example. But the main problem here is that in reality, no downward force is acting on the screw: it is just because the screw has helical-ring like structure that, on rotating, it moves downwards. If it was a nail instead of a screw, it would not have moved downwards at all. So I am not satisfied with this explanation of the rule, because it does not explain force acting on a moving charge due to applied field.
According to me, suppose A and B are two vectors forming an acute angle, where A is the base and B is the moving arm. Then
i) A.B means: Horizontal component of B, times A.
For example, F.s (=W) means how much distance is traveled by the object "in the direction" in which force F is applied on it.
The direction of resultant is the direction of force applied, F.
ii)A X B means: Vertical component of B, times A.
The direction of the resultant is always perpendicular to the plane in which A and B lie (How?).
Regarding magnetism, I know that a moving charge produces its own B-field, and this field is directly proportional to the velocity with which the charge is moving. The applied field only interacts with this magnetic field of the moving charge. Now as far as I know (using the right hand thumb rule), the magnetic field, if traced from N to S, is acting in the same direction of v, that is, in the direction the charge is moving. Now if the charge enters an applied magnetic field B, such that the applied field and v (or magnetic field of charge) is perpendicular to each other, then force acting on charge is max, by the formula:
F=q Bv sin 90=qBv
But how do these two magnetic fields interact?
Edit: I have deleted the diagram I had drawn earlier because it was a wrong one.
I am only familiar upto high school physics. So advanced maths won't make it easier for me. Please explain in simple terms. I will be grateful.
Thanks
Mr V
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