Calculating Full-Scale Deflection for Weakened Magnetic Field?

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The discussion focuses on calculating the current needed for full-scale deflection of a moving coil meter when the magnetic field is weakened to 80% of its original strength. Initially, a current of 50uA achieves full-scale deflection, but a decrease in the magnetic field means more current is required for the same deflection. The proposed solution suggests that 60uA would be needed, but the correct answer is actually 63uA due to the non-linear relationship between the decrease in magnetic field and the required increase in current. This discrepancy arises because a 20% decrease in magnetic field does not equate to a simple 20% increase in current. The discussion emphasizes the importance of understanding the mathematical relationships involved in such calculations.
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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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