Magnetic Field Strength (Integral needed)

[smellsey]

Homework Statement

You have 10 m of 0.55 mm diameter copper wire and a battery capable of passing 13 A through the wire. What magnetic field strength could you obtain inside a 2.8 cm diameter solenoid wound with the wire as closely spaced as possible?

Homework Equations

Turns of a solenoid = length of wire/ (2$$\pi$$ * radius of solenoid)

B = ( $$\mu$$*turns of a solenoid * Current)/($$\sqrt{}(4(radius of solenoid)^2+(radius of copper wire)^2$$ where $$\mu = 4\pi *10^-7$$

I believe that's right once you do the integration

The Attempt at a Solution

I tried to solve this and I got B = 0.27 T but it isn't right! I've tried over and over again, but I can't see to get the right answer.


Thanks!

 

[ideasrule]

Why do you need integration? Can't you use the formula for the magnetic field inside a solenoid?

 

[smellsey]

Well...you could be right. How would you do that?