Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN: 9780190698614
Author: Sadiku, Matthew N. O.
Publisher: Oxford University Press
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Chapter 9, Problem 35P

(a)

To determine

Find whether the field A=40sin(ωt+10x)az is a genuine EM field or not.

(a)

Expert Solution
Check Mark

Answer to Problem 35P

The field A=40sin(ωt+10x)az is a genuine EM field.

Explanation of Solution

Calculation:

Find A.

A=(xax+yay+zaz)[40sin(ωt+10x)az]=z[40sin(ωt+10x)]=0

Find ×A.

×A=|axayazxyz0040sin(ωt+10x)|=({y[40sin(ωt+10x)]}ax{x[40sin(ωt+10x)]}ay+0az)=0ax400cos(ωt+10x)ay+0az=400cos(ωt+10x)ay

As A=0 and ×A0, the given field is a genuine electromagnetic field.

Conclusion:

Thus, the field A=40sin(ωt+10x)az is a genuine EM field.

(b)

To determine

Find whether the field B=10ρcos(ωt2ρ)aϕ is a genuine EM field or not.

(b)

Expert Solution
Check Mark

Answer to Problem 35P

The field B=10ρcos(ωt2ρ)aϕ is a genuine EM field.

Explanation of Solution

Calculation:

Find B.

B=(ρaρ+θaθ+ϕaϕ)[10ρcos(ωt2ρ)aϕ]=ϕ[10ρcos(ωt2ρ)]=0

Find ×B.

×B=|aρaθaϕρθϕ0010ρcos(ωt2ρ)|=({θ[10ρcos(ωt2ρ)]}aρ{ρ[10ρcos(ωt2ρ)]}aθ+0aϕ)=0aρ{ρ[10ρcos(ωt2ρ)]}aθ+0aϕ0

As B=0 and ×B0, the given field is a genuine electromagnetic field.

Conclusion:

Thus, the field B=10ρcos(ωt2ρ)aϕ is a genuine EM field.

(c)

To determine

Find whether the field C=(3ρ2cotϕaρ+cosϕρaϕ)sin(ωt) is not a genuine EM field or not.

(c)

Expert Solution
Check Mark

Answer to Problem 35P

The field C=(3ρ2cotϕaρ+cosϕρaϕ)sin(ωt) is not a genuine EM field.

Explanation of Solution

Calculation:

Find C.

C=(ρaρ+θaθ+ϕaϕ)[(3ρ2cotϕaρ+cosϕρaϕ)sin(ωt)]=ρ[3ρ2cotϕsin(ωt)]+ϕ[cosϕρsin(ωt)]0

Find ×C.

×C=|aρaθaϕρθϕ3ρ2cotϕsin(ωt)0cosϕρsin(ωt)|=({θ[cosϕρsin(ωt)]}aρ{ρ[cosϕρsin(ωt)]ϕ[3ρ2cotϕsin(ωt)]}aθ+θ3ρ2cotϕsin(ωt)aϕ)0

As C0 and ×C0, the given field is not a genuine electromagnetic field.

Conclusion:

Thus, the field C=(3ρ2cotϕaρ+cosϕρaϕ)sin(ωt) is not a genuine EM field.

(d)

To determine

Find whether the field D=1rsinθsin(ωt5r)aθ is not a genuine EM field or not.

(d)

Expert Solution
Check Mark

Answer to Problem 35P

The field D=1rsinθsin(ωt5r)aθ is not a genuine EM field.

Explanation of Solution

Calculation:

Find D.

D=(rar+θaθ+ϕaϕ)[1rsinθsin(ωt5r)aθ]=θ[1rsinθsin(ωt5r)]0

Find ×D.

×D=|araθaϕrθϕ01rsinθsin(ωt5r)0|=({ϕ[1rsinθsin(ωt5r)]}ar0aθ+r[1rsinθsin(ωt5r)]aϕ)0

As D0 and ×D0, the given field is not a genuine electromagnetic field.

Conclusion:

Thus, the field D=1rsinθsin(ωt5r)aθ is not a genuine EM field.

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