Physics Exam > Physics Questions > Does the potential functionsatisfies the lapl...
Start Learning for Free
Does the potential function 
satisfies the laplace’s equations.
satisfies the laplace’s equations.- a)yes
- b)No
- c)yes for q = 3
- d)es if q → ∝
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
Does the potential functionsatisfies the laplace’s equations.a)y...
We have 
...(i)
...(ii)
and
...(iii)
Adding (1), (2) and (3)
i.e.
which is Laplace's equation. Thus the function
satisfies Laplace's equation.
...(i) ...(ii)and
...(iii)Adding (1), (2) and (3)
i.e.
which is Laplace's equation. Thus the function satisfies Laplace's equation.Most Upvoted Answer
Does the potential functionsatisfies the laplace’s equations.a)y...
Understanding Laplace's Equation
Laplace's equation is a second-order partial differential equation given by the formula: ∇²φ = 0. A function φ satisfies Laplace's equation if its Laplacian (the divergence of the gradient) is zero.
Given Potential Function
The potential function is defined as:
φ = q(x² + y² + z²)^(-1/2)
Calculating the Laplacian
To determine if φ satisfies Laplace's equation, we need to compute the Laplacian of φ.
1. Gradient Calculation:
- The gradient ∇φ involves partial derivatives of φ with respect to x, y, and z.
2. Divergence of the Gradient:
- The Laplacian is obtained by taking the divergence of the gradient calculated earlier.
Evaluating the Laplacian
When we compute the Laplacian for φ, we find that it simplifies to zero:
- The terms derived from the second derivatives of φ cancel out, confirming that ∇²φ = 0.
Conclusion
Since we verified that the Laplacian of the given potential function equals zero, we can conclude:
- The potential function φ = q(x² + y² + z²)^(-1/2) satisfies Laplace's equation universally, regardless of the value of q.
Thus, the correct answer is option 'A': Yes.
Laplace's equation is a second-order partial differential equation given by the formula: ∇²φ = 0. A function φ satisfies Laplace's equation if its Laplacian (the divergence of the gradient) is zero.
Given Potential Function
The potential function is defined as:
φ = q(x² + y² + z²)^(-1/2)
Calculating the Laplacian
To determine if φ satisfies Laplace's equation, we need to compute the Laplacian of φ.
1. Gradient Calculation:
- The gradient ∇φ involves partial derivatives of φ with respect to x, y, and z.
2. Divergence of the Gradient:
- The Laplacian is obtained by taking the divergence of the gradient calculated earlier.
Evaluating the Laplacian
When we compute the Laplacian for φ, we find that it simplifies to zero:
- The terms derived from the second derivatives of φ cancel out, confirming that ∇²φ = 0.
Conclusion
Since we verified that the Laplacian of the given potential function equals zero, we can conclude:
- The potential function φ = q(x² + y² + z²)^(-1/2) satisfies Laplace's equation universally, regardless of the value of q.
Thus, the correct answer is option 'A': Yes.
Free Test
FREE
| Start Free Test |
Community Answer
Does the potential functionsatisfies the laplace’s equations.a)y...
We have 
...(i)
...(ii)
and
...(iii)
Adding (1), (2) and (3)
i.e.
which is Laplace's equation. Thus the function
satisfies Laplace's equation.
...(i) ...(ii)and
...(iii)Adding (1), (2) and (3)
i.e.
which is Laplace's equation. Thus the function satisfies Laplace's equation.
|
Explore Courses for Physics exam
|
|
Does the potential functionsatisfies the laplace’s equations.a)yesb)Noc)yes for q = 3d)es if q→∝Correct answer is option 'A'. Can you explain this answer?
Question Description
Does the potential functionsatisfies the laplace’s equations.a)yesb)Noc)yes for q = 3d)es if q→∝Correct answer is option 'A'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Does the potential functionsatisfies the laplace’s equations.a)yesb)Noc)yes for q = 3d)es if q→∝Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Does the potential functionsatisfies the laplace’s equations.a)yesb)Noc)yes for q = 3d)es if q→∝Correct answer is option 'A'. Can you explain this answer?.
Does the potential functionsatisfies the laplace’s equations.a)yesb)Noc)yes for q = 3d)es if q→∝Correct answer is option 'A'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Does the potential functionsatisfies the laplace’s equations.a)yesb)Noc)yes for q = 3d)es if q→∝Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Does the potential functionsatisfies the laplace’s equations.a)yesb)Noc)yes for q = 3d)es if q→∝Correct answer is option 'A'. Can you explain this answer?.
Solutions for Does the potential functionsatisfies the laplace’s equations.a)yesb)Noc)yes for q = 3d)es if q→∝Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Physics.
Download more important topics, notes, lectures and mock test series for Physics Exam by signing up for free.
Here you can find the meaning of Does the potential functionsatisfies the laplace’s equations.a)yesb)Noc)yes for q = 3d)es if q→∝Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Does the potential functionsatisfies the laplace’s equations.a)yesb)Noc)yes for q = 3d)es if q→∝Correct answer is option 'A'. Can you explain this answer?, a detailed solution for Does the potential functionsatisfies the laplace’s equations.a)yesb)Noc)yes for q = 3d)es if q→∝Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of Does the potential functionsatisfies the laplace’s equations.a)yesb)Noc)yes for q = 3d)es if q→∝Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Does the potential functionsatisfies the laplace’s equations.a)yesb)Noc)yes for q = 3d)es if q→∝Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice Physics tests.
|
|
Explore Courses for Physics exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup