Question about two circular concentric coils

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SUMMARY

The discussion focuses on calculating the current required in an outer coil to achieve a net magnetic field of zero at the center of two concentric circular coils. The inner coil has 110 turns, a radius of 0.010 m, and carries a current of 5.6 A, while the outer coil has 190 turns and a radius of 0.014 m. The magnetic field produced by each coil can be expressed using the formula B = (constant) * I * N / (2 * R). By setting the magnetic fields equal and opposite, the current in the outer coil can be determined.

PREREQUISITES
  • Understanding of magnetic fields generated by current-carrying coils
  • Familiarity with the formula B = (constant) * I * N / (2 * R)
  • Basic algebra for solving equations
  • Knowledge of concentric coil configurations
NEXT STEPS
  • Calculate the magnetic field for the inner coil using the given parameters
  • Set the magnetic field equations for both coils equal to each other to find I2
  • Explore the effects of varying the number of turns in coils on magnetic field strength
  • Investigate the principles of superposition in magnetic fields
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Students studying electromagnetism, physics educators, and anyone interested in the practical applications of magnetic fields in coil systems.

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Homework Statement


Two circular coils are concentric and lie in the same plane. The inner coil contains 110 turns of wire, has a radius of 0.010 m, and carries a current of 5.6 A. The outer coil contains 190 turns and has a radius of 0.014 m. What must be the magnitude of the current in the outer coil, such that the net magnetic field at the common center of the two coils is zero?



Homework Equations


B=(constant)IN/2R


The Attempt at a Solution


Ok so I have I1=5.6 A
R1=.010 m
N1=110
R2=.014 m
N2=190
I2=?

I think that I have to use that equation somehow and set them equal to each other, but I'm lost after that. Perhaps I'm using the wrong equation entirely? Any help is much appreciated!

Edit: Do I just solve for B1 and then set that equal to the equation for the 2nd coil (only make it negative)?
 
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You should be able to figure the magnitude of the field from the first coil from what you're given.

Then they want to know what opposing current using the parameters of the other coil is needed to null out the B field at the center.

I find it easiest to keep it as variables of the 2 loops and then plug in the numbers at the end to solve for the one that you need.
 

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