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A solenoid that is 35 cm long and contains 450 circular coils 2.0 cm in diameter carries a 1.75-A current. (a) What is the magnetic field at the centre of the solenoid, 1.0 cm from the coils? (b) Suppose we now stretch out the coils to make a very long wire carrying the same current as before. What is the magnetic field 1.0 cm from the wire’s centre? Is it the same as that in part (a)? Why or why not?

Short Answer

Expert verified

A) The magnetic field at the center of the solenoid is2.83×103T B) The magnetic field at distance from the center of the wire is3.50×105T

Step by step solution

01

Concept of the magnetic field at the center of the solenoid

The magnetic field at the center of the solenoid is given by,Bsolenoid=μ0nln=NLthus,Bsolenoid=μ0NLI were where,μ0=4π×107H/mis permeability of free space, N is the number of turns, I is the current passing through the coil

02

Find the magnetic field at the center of the solenoid

Consider a solenoid which is L =35 cm long and contains N= 450 circular coils R =1.0 cm in radius, it carries a current of I =1.75 A. The magnetic field at the center of the solenoid is given by,Bsolenoid=μ0NL .Substitute the values in the given equation we have,

Bsolenoid=4π×107Tm/A4500.35(1.75A)=2.83×103T

Therefore, the magnetic field at the center of the solenoid is2.83×103T

03

STEP 3 Find the magnetic field at distance from the center of the wire

The magnetic field at distance of r=1.0 cm from the center of the wire. Assume that the wire is a very long wire. At distance r from a long straight wire, the magnetic field isBwire=μ0l2πr Substitute the values in the given equation we have,

Bwire=4π×107Tm/A×1.75A2π1.0×102m=3.50×105T

Therefore, the magnetic field at distance from the center of the wire is3.50×105T

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