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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

Figure 29-49 shows two very long straight wires (in cross section) that each carry a current of $4.00 A$ directly out of the page. Distance $d_{1} = 6.00 m$ and distance $d_{2} = 4.00 m$ . What is the magnitude of the net magnetic field at point P, which lies on a perpendicular bisector to the wires?

One long wire lies along an xaxis and carries a current of $30 A$ in the positive xdirection. A second long wire is perpendicular to the xyplane, passes through the point $(0, 4.0 m, 0)$ , and carries a current of $40 A$ in the positive zdirection. What is the magnitude of the resulting magnetic field at the point $(0, 2.0 m, 0)$ ?

A student makes a short electromagnet by winding of wire $300 turns$ around a wooden cylinder of diameter $d = 5.0 cm$ . The coil is connected to a battery producing a current of $4.0 A$ in the wire. (a) What is the magnitude of the magnetic dipole moment of this device? (b) At what axial distance d will the magnetic field have the magnitude $5 .0 渭罢$ (approximately one-tenth that of Earth鈥檚 magnetic field)?

The current-carrying wire loop in Fig. 29-60a lies all in one plane and consists of a semicircle of radius $10.0 c m$ , a smaller semicircle with the same center, and two radial lengths. The smaller semicircle is rotated out of that plane by angle $胃$ , until it is perpendicular to the plane (Fig.29-60b). Figure 29-60c gives the magnitude of the net magnetic field at the center of curvature versus angle $胃$ . The vertical scale is set by $B_{a} = 10.0 渭 T a n d B_{b} = 12.0 渭 T$ . What is the radius of the smaller semicircle?

In Figure, two long straight wires are perpendicular to the page and separated by distance $d_{1} = 0.75 cm$ . Wire 1 carries $6.5 A$ into the page. What are (a) magnitude and (b) direction (into or out of the page) of the current in wire 2 if the net magnetic field due to the two currents is zero at point P located at distance $d_{2} = 1.50 cm$ from wire 2?

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