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The Laplacian operator cannot be used in which one the following?
  • a)
    Two dimensional heat equation
  • b)
    Two dimensional wave equation
  • c)
    Poisson equation
  • d)
    Maxwell equation
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The Laplacian operator cannot be used in which one the following?a)Two...
Answer: d
Explanation: The first three options are general cases of Laplacian equation. Maxwell equation uses only divergence and curl, which is first order differential equation, whereas Laplacian operator is second order differential equation. Thus Maxwell equation will not employ Laplacian operator.
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Most Upvoted Answer
The Laplacian operator cannot be used in which one the following?a)Two...
Explanation:

Laplacian Operator:
The Laplacian operator, denoted by ∇^2 or Δ, is commonly used in mathematical physics to calculate the second spatial derivative of a function.

Maxwell's Equations:
Maxwell's equations describe the behavior of electric and magnetic fields. They consist of a set of four differential equations that form the foundation of classical electromagnetism.

Why Laplacian Operator cannot be used in Maxwell's Equations:
- Maxwell's equations involve time-dependent electric and magnetic fields, which include partial derivatives with respect to time.
- The Laplacian operator only involves spatial derivatives and does not account for time dependence.
- As Maxwell's equations are coupled partial differential equations involving both spatial and temporal derivatives, the Laplacian operator alone is not sufficient to describe their behavior.

Usage of Laplacian Operator in Other Equations:
- The Laplacian operator can be used in equations like the two-dimensional heat equation, wave equation, and Poisson equation, where only spatial derivatives are involved without any time dependence.
- In these cases, the Laplacian operator helps in describing the spatial distribution of quantities such as temperature, displacement, or potential.
Therefore, the Laplacian operator cannot be directly applied to Maxwell's equations due to their time-dependent nature, which requires a more comprehensive treatment involving both spatial and temporal derivatives.
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it depends on the length of the conductor the capacitance of the line is proportional to the length of the transmission line their effect is negligible on the performance of short having a length less than 80 km and low voltage transmission accidents of the transmission line along with the conductances forms the shunted mittens the conductance and the transmission line is because of the leakage over the surface of the conductor considered a line consisting of two conductors and be each of radius are the distance between the conductors being Des shown in the diagram below minus the potential difference between the conductors and via's work QA charge on conductor QB charge on conductor vvab pencil difference between conductor and the Epsilon minus absolute primitivity QA plus QV = 0 so that QA equals QB - equals DBA equals data equals DB equals our substituting these values and voltage equation we get the capacitance between the conductors is cab is referred to as lying to line capacitance if the two conductors are in VR oppositely charge then the potential difference between them is zero then the potential of each conductor is given by one half bath the capacitance between each conductor and point of zero potential and is capacitive CN is called the capacitance to neut or capacitance to ground capacitance cab is the combination of two equal capacity and VN series thus capacitance to neutral is twice the capacitance between the conductors IE CN equals to Cave the absolute primitivity Epsilon is given by Epsilon equals epsilono Epsilon are where epsilano is the permittivity of the free space and Epsilon or is the relative primitivity of the medium prayer capacitance reactants between one conductor and neutral capacitance of the symmetrical three phase line let a balanced system of voltage be applied to a symmetrical three-phase line shown below the phasor diagram of the three phase line with equilateral spacing is shown below take the voltage of conductor to neutral as a reference phaser the potential difference between conductor and we can be written the similarly potential difference between conductors and sea is on adding equations one and two we get also combining equation three and four from equation 6 and 7 the line to neutral capacitance the capacitance of symmetrical three phase line is same as that of the two wire line Related: Capacitance of Transmission Lines?

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The Laplacian operator cannot be used in which one the following?a)Two dimensional heat equationb)Two dimensional wave equationc)Poisson equationd)Maxwell equationCorrect answer is option 'D'. Can you explain this answer?
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