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Chapter 29: Q51P (page 836)

A 200−turnsolenoid having a length of25cmand a diameter of10cmcarries a current of0.29A. Calculate the magnitude of the magnetic field inside the solenoid.

Short Answer

Expert verified

The magnitude of the magnetic field inside the solenoid is 3×10-4T.

Step by step solution

01

Listing the given quantities

  • l=25 cm=0.25m
  • d=10 cm=0.10m
  • N=200
  • i=0.29A
02

Understanding the concept of magnetic field and solenoid  

We can calculate the magnetic field due to an ideal solenoid. In our case, the solenoid has a definite length, so we use this equation to calculate the magnetic field inside the solenoid.

Formula:

B=μ0in=μ0iNl

03

Calculate the magnitude of the magnetic field

We can calculate the magnetic field.

B=μ0in=μ0iNl=1.26×10-6×0.29×2000.25=2.92×10-4T≈3×10-4T

Hence, the magnitude of the magnetic field inside the solenoid is 3×10-4T.

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Most popular questions from this chapter

Figure 29-50ashows, in cross section, two long, parallel wires carrying current and separated by distance L. The ratio i1/i2 of their currents is4.00; the directions of the currents are not indicated. Figure 29-50bshows the ycomponent Byof their net magnetic field along the xaxis to the right of wire 2. The vertical scale is set by Bys=4.0nT , and the horizontal scale is set by xs=20.0cm . (a) At what value of x0 is Bymaximum?(b) If i2=3mA, what is the value of that maximum? What is the direction (into or out of the page) of (c) i1 and (d) i2?

Figure 29-84 shows a cross section of an infinite conducting sheet carrying a current per unit x-length of λ; the current emerges perpendicularly out of the page. (a) Use the Biot – Savart law and symmetry to show that for all pointsP above the sheet and all points P'below it, the magnetic fieldB→is parallel to the sheet and directed as shown. (b) Use Ampere’s law to prove that B=12·μ0λ at all points P andP'.

Figure 29-80 shows a cross-section of a long cylindrical conductor of radius a=4 cmcontaining a long cylindrical hole of radiusb=1.50cm. The central axes of the cylinder and hole are parallel and are distanced=2cmapart; currentis uniformly distributed over the tinted area. (a) What is the magnitude of the magnetic field at the center of the hole? (b) Discuss the two special casesb=0andd=0.

Eight wires cut the page perpendicularly at the points shown in Figure 29-70 wire labeled with the integer k(k=1,2,...,8)carries the current ki, where i=4.50mA. For those wires with odd k, the current is out of the page; for those with even k, it is into the page. Evaluate∮B→.ds→ along the closed path in the direction shown.

What is the magnitude of the magnetic dipole moment μ→ of the solenoid described in Problem 51?
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