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?

 

[thomate1]

There may be a mistake in your calculation of the flux linkage. The correct equation for flux linkage is:

Flux linkage = number of turns * magnetic flux

In this case, the number of turns is given as 500, and the magnetic flux is given by the product of magnetic flux density and area. So the correct calculation would be:

Flux linkage = 500 * (3*10^-3) * (2*10^-4) = 3*10^-1 Wb

This is equivalent to 3*10^-4 Wb, as given in the book. Double check your calculation to make sure you are using the correct equation and plugging in the correct values.