• Support PF! Buy your school textbooks, materials and every day products via PF Here!

An Air-Filled Toroidal Solenoid

  • Thread starter GreenMind
  • Start date
6
0
1. Homework Statement
179190.jpg

An air-filled toroidal solenoid has a mean radius of 14.5 cm and a cross-sectional area of 4.99 cm^2 (see the figure). The current flowing through it is 11.7 A, and it is desired that the energy stored within the solenoid be at least 0.388 J.

What is the least number of turns that the winding must have?
Express your answer numerically, as a whole number, to three significant figures.

2. Homework Equations

[tex] B = \frac {\mu_0 N I}{2 \Pi r} [/tex]

[tex] \Phi_B = \oint \vec{B} \cdot \vec{dA}[/tex]

[tex] U = \frac {1}{2} L I^2[/tex]

[tex] L = \frac {N \Phi_B}{i}[/tex]

3. The Attempt at a Solution

Solved for N to get the Number of Turns.

[tex] N = \sqrt{\frac {4 (\Pi) U r}{\mu_0 I^2 A}}[/tex]

[tex] N = \sqrt{\frac {(4) (\Pi) (0.388j) (0.145m)}{(4 (\Pi) (10^{-7}) \frac{wb}{Am}) (11.7A^2) (0.0499m^2)}}[/tex]

N = 287 turns

Do I have some conversion wrong or did I miss something.
 
Last edited:
6
0
SOLVED!

Found my error in my conversion of [tex]cm^2[/tex] to [tex]m^2[/tex].

I did my the correct conversion is [tex] \frac{4.99}{10000} [/tex]
 

Related Threads for: An Air-Filled Toroidal Solenoid

  • Posted
Replies
0
Views
2K
  • Posted
Replies
4
Views
2K
  • Posted
Replies
0
Views
1K
  • Posted
Replies
2
Views
907
  • Posted
Replies
0
Views
6K
  • Posted
Replies
5
Views
4K
Replies
3
Views
4K

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top