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Chapter 29: Q52P (page 861)

A solenoid $1.30$ long and $2.60 cm$ in diameter carries a current of $1.80 A$ . The magnetic field inside the solenoid is $23.0 mT$ . Find the length of the wire forming the solenoid.

Short Answer

Expert verified

The length of the wire forming the solenoid is $108 m$ .

Step by step solution

01

Listing the given quantities

$l = 1.30 m$

$d = 2.60 cm = 0.0260 m$

$B = 23 mT = 0.023 T$

$i = 18 A$

02

Understanding the concept of magnetic field and solenoid

We find the number of turns of the solenoid. Using the number of turns, we can find the total length of the wire used in making the solenoid.

$B = 渭_{0} in = 渭_{0} i (\frac{N}{l})$

03

Calculations of the length of the wire forming the solenoid

The number of turns of the solenoid is

$B = 渭_{0} i (\frac{N}{l})$

$\frac{N}{l} = \frac{B}{渭_{0} i}$

$\begin{matrix} N = \frac{Bl}{渭_{0} i} \\ = \frac{0.023 脳 1.30}{1.26 脳 10^{鈭� 6} 脳 18} \\ 鈮� 1322 \end{matrix}$

As we know that the length of the circular loop is the circumference of that loop. So, the total length of the solenoid is

$L = 2 蟺谤狈$

Since $r = \frac{d}{2}$

Thus,

$\begin{matrix} L = 2 蟺脳 \frac{0.0260}{2} 脳 1322 \\ = 蟺脳 0.0260 脳 1322 \\ = 107.98 \\ 鈮� 108 m \end{matrix}$

The length of the wire forming the solenoid is $108 m$ .

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Most popular questions from this chapter

A surveyor is using a magnetic compass $6.1 m$ below a power line in which there is a steady current of $100 A$ .(a) What is the magnetic field at the site of the compass due to the power line? (b) Will this field interfere seriously with the compass reading? The horizontal component of Earth鈥檚 magnetic field at the site is role="math" localid="1663130453654" $20 mT$ .

Figure 29-45 shows two current segments. The lower segment carries a current of $i_{1} = 0.40 A$ and includes a semicircular arc with radius $5.0 cm$ , angle $180 掳$ , and center point P. The upper segment carries current $i_{2} = 2 i_{1}$ and includes a circular arc with radius $4.0 cm$ , angle $120 掳$ , and the same center point P. What are the(a) magnitude and (b) direction of the net magnetic field at Pfor the indicated current directions? What are the (c)magnitude of if i₁ is reversed and (d) direction $\overset{鈫�}{B}$ of if i₁ is reversed?

Figure 29-25 represents a snapshot of the velocity vectors of four electrons near a wire carrying current i. The four velocities have the same magnitude; velocity is directed into the page. Electrons 1 and 2 are at the same distance from the wire, as are electrons 3 and 4. Rank the electrons according to the magnitudes of the magnetic forces on them due to current i, greatest first.

Each of the eight conductors in Figure carries $2.0 A$ of current into or out of the page. Two paths are indicated for the line integral. $鈭� \overset{鈫�}{B} . \overset{鈫�}{d s}$ (a) What is the value of the integral for path 1 and (b) What is the value of the integral for path 2?

The current density $\overset{鈫�}{J}$ inside a long, solid, cylindrical wire of radius a=3.1mm is in the direction of the central axis, and its magnitude varies linearly with radial distance rfrom the axis according to $J = J_{0} r / a,$ where $J_{0} = 310 A / m^{2}$ . (a) Find the magnitude of the magnetic field at role="math" localid="1663132348934" $r = 0$ , (b) Find the magnitude of the magnetic field $r = a / 2$ , and(c) Find the magnitude of the magnetic field $r = a$ .

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