Flux Linkage with a coil in a solenoid

[BadlyAddicted]

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

 

[alphysicist]

Hi BadlyAddicted,

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?