Understanding the Force on a Current-Carrying Conductor: Explained

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The force on a current-carrying conductor is given by the equation F = BIL sin(θ), where θ is the angle between the conductor's length (L) and the magnetic field (B). The discussion clarifies that the focus should be on the component of the product IL that is perpendicular to B, rather than treating current (I) and length (L) as separate vectors. It emphasizes that the current follows the wire, making it essential to consider the effective length at right angles to the magnetic field. The vertical component of the length represents the distance through which the current travels at 90 degrees to B, while the parallel component can be disregarded. Understanding this relationship is crucial for accurately calculating the force on the conductor.
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The force on a current carrying conducter is F=BIL sin@ . One book tells me that you do this because you need to find the component of I at 90 degrees to B. Yet another says you need to find the component of L at 90 degrees to B. Obviously you don't work out BxIsin@xLsin@, so you don't work out both components.

So I was wondering, are you really just working out the component of the quantity IxL that is at right angles to B?
 
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Don't think of "I" and "L" as separate vectors. The current (I) follows the wire (L).

Think of the force as F = I L X B = ILBsinθ; where θ is the angle between L and B; I is a scalar.
 
Yeah. I guess if you work out the vertical component of the length, that is the vertical distance through which the current has travelled, i.e. the distance through which it is at 90 degrees to B, and the horizontal distance can be forgotten as it is parallel to B. That makes sense.
 

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