
(a)
State whether the given potential satisfies Laplace’s equation or not.
(a)

Answer to Problem 10P
No, the given potential does not satisfy Laplace’s equation.
Explanation of Solution
Calculation:
Consider the given potential expression.
Write the expression for
Substitute Equation (1) in (2).
Write the expression for the Laplace’s equation.
Equation (2) is not equal to Laplace’s equation in Equation (4). Hence, the given potential equation does not satisfy the Laplace’s equation.
Conclusion:
No, the given potential does not satisfy Laplace’s equation.
(b)
State whether the given potential satisfies Laplace’s equation or not.
(b)

Answer to Problem 10P
Yes, the given potential satisfies Laplace’s equation.
Explanation of Solution
Calculation:
Consider the given potential expression.
Write the expression for the Laplace’s equation in cylindrical coordinates.
Substitute Equation (5) in (6).
Simplify the equation as follows:
Hence, the given potential equation satisfies the Laplace’s equation.
Conclusion:
Yes, the given potential satisfies Laplace’s equation.
(c)
State whether the given potential satisfies Laplace’s equation or not.
(c)

Answer to Problem 10P
No, the given potential does not satisfy Laplace’s equation.
Explanation of Solution
Calculation:
Consider the given potential expression.
Write the expression for the Laplace’s equation in spherical coordinates.
Substitute Equation (7) in (8).
Hence, the given potential equation does not satisfy the Laplace’s equation.
Conclusion:
No, the given potential does not satisfy Laplace’s equation.
Want to see more full solutions like this?
Chapter 6 Solutions
Elements Of Electromagnetics
- Determine the magnitude of the minimum force P needed to prevent the 20 kg uniform rod AB from sliding. The contact surface at A is smooth, whereas the coefficient of static friction between the rod and the floor is μs = 0.3.arrow_forwardDetermine the magnitudes of the reactions at the fixed support at A.arrow_forwardLet Hill frame H = {i-hat_r, i-hat_θ, i-hat_h} be the orbit frame of the LMO satellite. These base vectors are generally defined as:i-hat_r = r_LM / |r_LM|, i-hat_theta = i-hat_h X i-hat_r, i-hat_h = r_LM X r-dot_LMO /( | r_LM X r-dot_LMO | ) How would you: • Determine an analytic expressions for [HN]arrow_forward
- De Moivre’s Theoremarrow_forwardhand-written solutions only, please.arrow_forwardDetermine the shear flow qqq for the given profile when the shear forces acting at the torsional center are Qy=30Q_y = 30Qy=30 kN and Qz=20Q_z = 20Qz=20 kN. Also, calculate qmaxq_{\max}qmax and τmax\tau_{\max}τmax. Given:Iy=10.5×106I_y = 10.5 \times 10^6Iy=10.5×106 mm4^44,Iz=20.8×106I_z = 20.8 \times 10^6Iz=20.8×106 mm4^44,Iyz=6×106I_{yz} = 6 \times 10^6Iyz=6×106 mm4^44. Additional parameters:αy=0.5714\alpha_y = 0.5714αy=0.5714,αz=0.2885\alpha_z = 0.2885αz=0.2885,γ=1.1974\gamma = 1.1974γ=1.1974. (Check hint: τmax\tau_{\max}τmax should be approximately 30 MPa.)arrow_forward
- hand-written solutions only, please.arrow_forwardIn the bending of a U-profile beam, the load path passes through the torsional center C, causing a moment of 25 kNm at the cross-section under consideration. Additionally, the beam is subjected to an axial tensile force of 100 kN at the centroid. Determine the maximum absolute normal stress.(Check hint: approximately 350 MPa, but where?)arrow_forward### Make an introduction to a report of a rocket study project, in the OpenRocket software, where the project consists of the simulation of single-stage and two-stage rockets, estimating the values of the exhaust velocities of the engines used, as well as obtaining the graphs of "altitude", "mass ratio x t", "thrust x t" and "ψ × t".arrow_forward
- A 6305 ball bearing is subjected to a steady 5000-N radial load and a 2000-N thrust load and uses a very clean lubricant throughout its life. If the inner race angular velocity is 500 rpm find The equivalent radial load the L10 life and the L50 lifearrow_forwardWhere on the below beam is the Maxiumum Slope likely to occur? C A; Атят Barrow_forwardWhat is the moment of Inertia of this body? What is Ixx, Iyy, and Izzarrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY





