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Chapter 29: Q52P (page 861)

A solenoid 1.30 long and2.60cm in diameter carries a current of 1.80A. The magnetic field inside the solenoid is 23.0mT . Find the length of the wire forming the solenoid.

Short Answer

Expert verified
  1. The length of the wire forming the solenoid is 108m.

Step by step solution

01

Listing the given quantities 

l=1.30m

d=2.60cm=0.0260m

B=23mT=0.023T

i=18A

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=μ0in=μ0iNl

03

Calculations of the length of the wire forming the solenoid  

The number of turns of the solenoid is

B=μ0iNl

Nl=Bμ0i

N=Blμ0i=0.023×1.301.26×10−6×18≈1322

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=2πrN

Since r=d2

Thus,

L=2π×0.02602×1322=π×0.0260×1322=107.98≈108m

The length of the wire forming the solenoid is108m .

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