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Chapter 22: Q65PE (page 814)

What current is needed in the solenoid described in Exercise 22.58 to produce a magnetic field 104 times the Earth鈥檚 magnetic field of 5.00脳10-5T?

Short Answer

Expert verified

The current required in a 10,000 turn solenoid to generate 104times Earth's magnetic field is 39.8A .

Step by step solution

01

Definition of magnetic field

A magnetic field is defined as a position in space near a magnet or an electric current where a physical field is formed by a moving electric charge applying force on another moving electric charge.

02

Given information and formula to use

The number of turns per meter is,n=10000

The produced magnetic field is,

B=104脳5.00脳105T=0.500T

The magnetic field inside a solenoid can be expressed as,

B=渭0nl鈥︹赌︹赌︹赌︹赌︹赌�(1)

Where 渭0is the magnetic permeability in the free space.

03

Step 3: The required current

Rearranging the equation (1) and substituting the given data, we will get

I=B渭0n=0.500T4蟺脳10-7N/m2脳10000=39.8A

Therefore, the current required in a 10,000 turn solenoid to generate 104times Earth's magnetic field is 39.8 A .

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