Chapter 29: Q. 44 (page 832)

At what distance on the axis of a current loop is the magnetic field half the strength of the field at the center of the loop? Give your fanswer as a multiple of $R$ .

Short Answer

Expert verified

The strenght of the field at the center of the loop as multiple of $R$ islocalid="1651061635560" $z = 0.77 R$ .

Step by step solution

Given information

We need to find the distance on the axis of a current loop is the magnetic field half the strength of the field at the center of the lgoop.

Calculation

Megnatic field at $z$ from center is $B$

localid="1651722030019" $B = \frac{μ_{o} I R^{2}}{2 {(z^{2} + R^{2})}^{3 / 2}} B_{c e n t e r} = \frac{μ_{o} I}{2 R}$

As per the questions

$B_{z} = \frac{B c}{c} \frac{μ_{o} I}{2 R} \times \frac{1}{2} = \frac{μ_{o} I R^{2}}{2 {(z^{2} + R^{2})}^{\frac{3}{2}}} \frac{1}{2 R} = \frac{R^{2}}{{(z^{2} + R^{2})}^{\frac{3}{2}}} 2 R^{3} = {(z^{2} + R^{2})}^{\frac{3}{2}} 2^{\frac{1}{3}} R = {(z^{2} + R^{2})}^{\frac{1}{2}} 2^{\frac{2}{3}} R^{2} = z^{2} + R^{2} z^{2} = (4^{\frac{1}{3}} - 1) R^{2} z = \sqrt{\sqrt[3]{4 - 1}} R$

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At what distance on the axis of a current loop is the magnetic field half the strength of the field at the center of the loop? Give your fanswer as a multiple of $R$ .

Short Answer

Step by step solution

Given information

Calculation

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At what distance on the axis of a current loop is the magnetic field half the strength of the field at the center of the loop? Give your fanswer as a multiple of R.

Short Answer

Step by step solution

Given information

Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Solid State Physics

Magnetism and Electromagnetic Induction

Quantum Physics

Electrostatics

Translational Dynamics

Geometrical and Physical Optics

Study anywhere. Anytime. Across all devices.

At what distance on the axis of a current loop is the magnetic field half the strength of the field at the center of the loop? Give your fanswer as a multiple of $R$ .