Calculating Full-Scale Deflection for Weakened Magnetic Field?

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SUMMARY

The discussion focuses on calculating the current required for full-scale deflection in a moving coil meter when the magnetic field strength is reduced to 80% of its original value. The original full-scale deflection occurs at 50µA, but due to the weakened magnetic field, a higher current is necessary to achieve the same deflection. The correct calculation reveals that the required current is 63µA, as the relationship between magnetic field strength and current is not linear; a 20% decrease in magnetic field strength does not equate to a simple 20% increase in current.

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Homework Statement


The needle of a moving coil meter gives a full-scale deflection for a current of 50uA. What current would give a full-scale deflection if the magnetic field weakened to 80% of its original value?


Homework Equations





The Attempt at a Solution


Decrease magnetic field => needle not deflected as much for a given current such as 50uA. A full-scale deflection now would result in 20% more current than before because of the 20% decrease in magnetic field. I assume the powers of magnetic strength and current are equal and unity. So now 50uA*1.2=60uA would result. However the answers suggested 63uA. Why?
 
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Because "a 20% decrease" and a "20% increase" are not the inverse of each other.

0.8 times 1.2 = 0.96, not 1.0

Your basic idea about how to solve the problem is OK.
 
That is good. It's liitle things like this that tests your mathematical intuition. For me, it's obviously not very good but I'm working on it.
 

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