Concept explainers
The solution of Laplace' equation.
Answer to Problem 6.43P
The potential field
Explanation of Solution
Calculation:
The Poisson's equation (generalization of Laplace equation) is defined for
The Poisson's equation is written as
Here,
Simplify equation (1) as,
Integrate equation (2) with respect to spherical coordinate
Substitute
Simplified the equation (4) as,
The Laplace's equation is defined for
The Laplace's equation is written as
Integrate the equation (5) with respect to spherical coordinate
Equation (6) is multiplied with
If equation (6) and equation (7) is equal, then it is written as
Simplified the equation (8) as,
Substitute
At boundary condition
Substitute
Simplify equation (12) as
Integrate the equation (3) with respect to
Substitute
Simplify equation (14) as
Integrate the equation (10) with respect to
Substitute
Equation (16) is simplified as
Substitute
Substitute
If equation (17) and equation (18) is equal, then it is written as
Substitute
Substitute
Substitute
The value of potential difference
Substitute
Substitute
Conclusion:
Therefore, the potential field
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Chapter 6 Solutions
Engineering Electromagnetics
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- Suppose a eopper conductor of lengin uym ana cross-sectional area (A)m and resistivity On m, its resistance is [R = p(/A)). This copper conductor wounded around a ferTomagnetic core, forming (N) turns. When this coil fed by a DC voltage (V), its steady state current will be [lde = (Vac/R)]. But when this coil fed by an ms value of an AC voltage (Vms = Vac), a steady state AC current of an rms value (Ia) will pass through it. Explain the following questions: a) Why (lacarrow_forwarda conductor moving with a velocity of 5.0 m/s to the right in the presence of a magnetic field. The flux density is 0.5 T into the page, and the wire is 1.0 m in length, oriented as shown. What are the magnitude resulting induced voltage?arrow_forwardSuppose a eopper conductor of lengin ym ana cross-sectional area (A)m and resistivity On m, its resistance is [R = p(/A)). This copper conductor wounded around a ferTomagnetic core, forming (N) turns. When this coil fed by a DC voltage (V), its steady state current will be [lde = (Vac/R)]. But when this coil fed by an ms value of an AC voltage (Vms = Vac), a steady state AC current of an rms value (Ia) will pass through it. Explain the following questions: a) Why (lacarrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_iosRecommended textbooks for you
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