Flux Linkage with a coil in a solenoid

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SUMMARY

The discussion centers on calculating the magnetic flux linkage in a solenoid with a cross-sectional area of 2 x 10^-4 m², a length of 0.5 m, and 500 turns. The required current to achieve a magnetic flux density of 3 x 10^-3 Tesla is determined to be 2.39 A. However, the initial calculation for flux linkage, derived from the formula flux linkage = magnetic flux density * Area, resulted in 6 x 10^-7 Webers, which is incorrect. The correct flux linkage for the entire solenoid is 3 x 10^-4 Webers, necessitating further calculation involving the total number of turns.

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  • Understanding of solenoid physics and magnetic fields
  • Familiarity with the formula for magnetic flux density
  • Knowledge of the concept of flux linkage in electromagnetism
  • Basic algebra for manipulating equations
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Homework Statement


A solenoid of cross-sectional area 2*10^-4 m^2 and length 0.5m having 500 turns is to be used to produce a uniform magnetic field some distance close to the center of the solenoid. Find the current that must flow in the solenoid to produce a magnetic flux density of 3*10^-3 Tesla. What is the flux linage with the coil?

2. The attempt at a solution

I worked out the first part. I found the current and it is 2.39A (correct according to the answer given by the book)

Now the second part, i used the equation flux linkage = magnetic flux density * Area
= (3 * 10 ^-3) * (2*10^-4)
= 6*10^-7 Webers

Apparently my second answer is incorrect. According to the book it's supposed to be 3*10^-4 Wb. Can someone please help me find my mistake? Thanks a lot
 
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Hi BadlyAddicted,

BadlyAddicted said:

Homework Statement


A solenoid of cross-sectional area 2*10^-4 m^2 and length 0.5m having 500 turns is to be used to produce a uniform magnetic field some distance close to the center of the solenoid. Find the current that must flow in the solenoid to produce a magnetic flux density of 3*10^-3 Tesla. What is the flux linage with the coil?

2. The attempt at a solution

I worked out the first part. I found the current and it is 2.39A (correct according to the answer given by the book)

Now the second part, i used the equation flux linkage = magnetic flux density * Area
= (3 * 10 ^-3) * (2*10^-4)
= 6*10^-7 Webers

That's right for the flux through one loop of the solenoid. So how would you find the flux linkage for the entire solenoid?
 

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