Reasoning Problem 20.74 A magnetic field B = 1 T is considered to be a strong fi

Question

Reasoning Problem 20.74

A magnetic field B = 1 T is considered to be a strong field. If you want to produce this field using a single loop of wire wound around a pencil, what must the current be?

Part 1 - Recognize the Principles

The magnetic field at the center of a current loop depends on the radius of the loop, and the magnitude of the current. To produce a large field with a single loop requires an extremely large current. The point of this problem is to find how large the current must be.

Part 2 - Sketch the Problem

Part 3 - Identify the Relationships

Which of the following relations gives the magnetic field at the center of a current loop of radius R carrying a current I? ?0I 2?R ?0I 2R      ?0I R ?0I 2?R ?0I 2R      ?0I R ?0I 2?R ?0I 2R ?0I R

Part 4 - Solve

Estimate To evaluate your expression for the magnetic field in Part 3, you need a value for the radius of the current loop. What is a reasonable estimate for the radius of a pencil?
mm
Calculations (use your estimate) Using your estimate for R, what current would be needed to produce a magnetic field of 1 T at the center of the loop?
A
To evaluate your expression for the magnetic field in Part 3, you need a value for the radius of the current loop. What is a reasonable estimate for the radius of a pencil?
mm Using your estimate for R, what current would be needed to produce a magnetic field of 1 T at the center of the loop?
A

Part 5 - What Does It Mean?

This is an extremely large current. In fact, it would probably melt any wire that you could manage to wrap around a pencil! It is hard to generate large magnetic fields without using large currents. ?0I 2?R

Explanation / Answer

Part 3 - Identify the Relationships

Which of the following relations gives the magnetic field at the center of a current loop of radius R carrying a current I? u0 i/2R

Part 4 - Solve

Estimate To evaluate your expression for the magnetic field in Part 3, you need a value for the radius of the current loop. What is a reasonable estimate for the radius of a pencil?
2 mm

Calculations (use your estimate) Using your estimate for R, what current would be needed to produce a magnetic field of 1 T at the center of the loop?
i = 2RB/u0 = 2*2e-3*1/(4*3.1416e-7) = 3183 A
To evaluate your expression for the magnetic field in Part 3, you need a value for the radius of the current loop. What is a reasonable estimate for the radius of a pencil?
2 mm
Using your estimate for R, what current would be needed to produce a magnetic field of 1 T at the center of the loop?
i = 2RB/u0 = 2*2e-3*1/(4*3.1416e-7) = 3183 A

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