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Chapter 28: Q58P (page 832)

The magnetic dipole moment of Earth has magnitude8.00×1022J/T . Assume that this is produced by charges flowing in Earth’s molten outer core. If the radius of their circular path is 3500 km, calculate the current they produce.

Short Answer

Expert verified

i=2.08×109A

Step by step solution

01

Given

The radius of the earth=r=3500km=3500×103m

The magnetic dipole moment of the earth = μ=8.00×1022J/T

02

Understanding the concept

The charges flowing in the molten outer core of the earth produce the magnetic dipole moment. The current produced by the charges can be calculated by substituting the given quantities in the formula for magnetic dipole moment.

μ=NiA

03

Calculate the current produced

The magnetic dipole moment is calculated as

μ=NiA

Here,N=1andA=πr2

μ=iπ2

Rearranging the equation to find the value of the current.

i=μπr2i=8.00×10223.14×3500×1032i=2.08×109A

Hence, i=2.08×109A

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Most popular questions from this chapter

Anelectronfollowsahelicalpathinauniformmagneticfieldofmagnitude0.300T.Thepitchofthepathis6.00µm,andthemagnitudeofthemagneticforceontheelectronis2.00×10-15N.Whatistheelectron’sspeed?

In Figure 28-39, a charged particle moves into a region of uniform magnetic field, goes through half a circle, and then exits that region. The particle is either a proton or an electron (you must decide which). It spends 130 ns in the region. (a)What is the magnitude of B→?

(b)If the particle is sent back through the magnetic field (along the same initial path) but with 2.00 times its previous kinetic energy, how much time does it spend in the field during this trip?

A proton of charge +eand mass menters a uniform magnetic field B⃗=Bi^ with an initial velocityv⃗=v0xi^+v0yj^.Find an expression in unit-vector notation for its velocity at any later time t.

Two concentric, circular wire loops, of radii r1 = 20.0cm and r2 = 30.0 cm, are located in an xyplane; each carries a clockwise current of 7.00 A (Figure).

(a) Find the magnitude of the net magnetic dipole moment of the system.

(b) Repeat for reversed current in the inner loop.

A proton, a deuteron (q=+e, m=2.0u), and an alpha particle (q=+2e, m=4.0u) are accelerated through the same potential difference and then enter the same region of uniform magnetic field, moving perpendicular to . What is the ratio of (a) the proton’s kinetic energy Kp to the alpha particle’s kinetic energy Ka and (b) the deuteron’s kinetic energy Kd to Ka? If the radius of the proton’s circular path is 10cm, what is the radius of (c) the deuteron’s path and (d) the alpha particle’s path
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