Question

You have a 1.0-m-long copper wire. You want to make an
N-turn current loop that generates a 1.0 mT magnetic field at the
center when the current is 1.0 A. You must use the entire wire.
'What will be the diameter of your coil?

Answer 1

Question #75233, Physics / Electromagnetism

You have a 1.0-m-long copper wire. You want to make an N-turn current loop that generates a 1.0 mT magnetic field at the center when the current is 1.0 A. You must use the entire wire. 'What will be the diameter of your coil?'

Need to calculate:

d - ?

$$l = 1.0 \text{ m}$$ $$B = 1.0 \text{ mT} = 10^{-3} \text{ T}$$ $$I = 1.0 \text{ A}$$ $$\mu_0 = 4\pi \cdot 10^{-7} \text{ N} \cdot A^{-2}$$

Solution:

The field for coil is $B = \frac{N\mu_0I}{d}$ (a). Wire length $= N2\pi r = N\pi d, N = \frac{l}{\pi d}$.

Sub into (a) $= \frac{l\mu_0I}{\pi d^2}$. Then $d^2 = \frac{l\mu_0I}{B} \rightarrow d = \sqrt{\frac{l\mu_0I}{B}}$.

$$d = \sqrt{\frac{1.0 \cdot 4\pi \cdot 10^{-7} \cdot 1.0}{10^{-3}}} = 0.035 \text{ m}$$

Answer: $d = 0.035 \text{ m}$

Answer provided by https://www.AssignmentExpert.com