Energy density of magnetic field in a solenoid

[mdf730]

Homework Statement

A solenoid that is 117 cm long has a cross-sectional area of 20.0 cm2. There are 1010 turns of wire carrying a current of 9.56 A. (a) Calculate the energy density of the magnetic field inside the solenoid. (b) Find the total energy in joules stored in the magnetic field there (neglect end effects).

Homework Equations

B = μo*n*I, where n=N/l
energy density = B^2/(2*μo)
total energy = answer to part a times the volume

The Attempt at a Solution

Plugging the formulas into each other, I got

(((1010/1.17)*9.56*4*10^-7)^2)/(8*10^-7) = 13.6 J/m^3 for part (a) and
13.6*.2*1.17 = 3.19 for part (b)

Both are incorrect.

 

[BruceW]

for part a, you have used μo to be 4*10^-7 but this is not the right definition. And for part b, 20cm^2 is not equal to 0.2m^2 (remember that 100cm^2 is not 1m^2). Apart from that, your working looks good.

 

[mdf730]

Oh, thank you! I hate when I miss stupid little things like that.

 

[BruceW]

hehe. yeah it is annoying when that happens.

 

[Nickie]

I would approach this problem by first checking my calculations and making sure that I have used the correct units for all of the variables. I would also double check the given values to ensure accuracy.

Next, I would analyze the equations being used and make sure that they are applicable to the given scenario. In this case, the equations for magnetic field and energy density are correct, but the formula for total energy may need to be adjusted for a solenoid.

I would also consider any assumptions that are being made, such as neglecting end effects, and how they may affect the accuracy of the calculations. If necessary, I would research and use more advanced equations or techniques to account for these effects.

Lastly, I would consider the limitations of the given information and how they may affect the accuracy of the results. For example, the given cross-sectional area may not account for the thickness of the wire, which could affect the magnetic field and energy density calculations.

Overall, as a scientist, I would carefully review and analyze all aspects of the problem to ensure accurate and reliable results.