torque related to current?

[MrNeuro]

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the torque formula thats sorta messing with my head in how it relates to Faraday's law is the following

𝝉=IABcosϴ

where

I = 𝝉/ABcosϴ

according to this rearrangement current increases with decreasing area and magnetic field perp to loop

but according to faradays law a larger current is induced with a larger B and A so how does this tie into the I seen in the torque formula?

 

[MedPR]

the torque formula thats sorta messing with my head in how it relates to Faraday's law is the following

𝝉=IABcosϴ

where

I = 𝝉/ABcosϴ

according to this rearrangement current increases with decreasing area and magnetic field perp to loop

but according to faradays law a larger current is induced with a larger B and A so how does this tie into the I seen in the torque formula?

More current indirectly increases torque on a dipole within a magnetic field. More current = stronger field. Stronger field = stronger field force. Stronger force = more torque as you probably already know from normal (read: non-electromagnetic) torque.

 

[MrNeuro]

More current indirectly increases torque on a dipole within a magnetic field. More current = stronger field. Stronger field = stronger field force. Stronger force = more torque as you probably already know from normal (read: non-electromagnetic) torque.

yeah i get all that

but what im asking is according to the torque formula if you increase B or A you decrease current which is shouldn't be true why does that formula say that???

 

[Bah9p8]

yeah i get all that

but what im asking is according to the torque formula if you increase B or A you decrease current which is shouldn't be true why does that formula say that???

To try to untwist your head, think about if you were setting this experiment up in real life. Your torque would have to be your dependent variable, since it's completely dependent on everything; you have no control over it directly.
You're getting confused by keeping torque constant while changing area and current. If you doubled the area of the loop, current would have to be cut in half to maintain the same torque.