Physics Exam > Physics Questions > If electric field hat E = i + j + k where i, ...
Start Learning for Free
If electric field hat E = i + j + k where i, j and k are the unit vectors in three-dimensions, the value of divergence of E is:
(a)-3
(b) 2
(c) 0
(d) 3?
(a)-3
(b) 2
(c) 0
(d) 3?
Most Upvoted Answer
If electric field hat E = i + j + k where i, j and k are the unit vect...
Understanding Electric Field and Divergence
The electric field vector given is E = i + j + k. To find the divergence of this electric field, we need to apply the mathematical operation known as divergence.
Divergence Definition
The divergence of a vector field F = (F1, F2, F3) in three-dimensional space is calculated using the formula:
∇·F = ∂F1/∂x + ∂F2/∂y + ∂F3/∂z
Where:
- F1, F2, and F3 are the components of the vector field along the x, y, and z axes respectively.
- ∂ denotes partial differentiation.
Components of the Electric Field
For the electric field E = i + j + k, we can identify the components as:
- F1 = 1 (coefficient of i)
- F2 = 1 (coefficient of j)
- F3 = 1 (coefficient of k)
Calculating the Divergence
Now we apply the divergence formula:
- ∂F1/∂x = ∂(1)/∂x = 0
- ∂F2/∂y = ∂(1)/∂y = 0
- ∂F3/∂z = ∂(1)/∂z = 0
Putting these together, we get:
∇·E = 0 + 0 + 0 = 0
Conclusion
The divergence of the electric field E = i + j + k is:
- The result is 0.
Therefore, the correct answer to the question is (c) 0.
The electric field vector given is E = i + j + k. To find the divergence of this electric field, we need to apply the mathematical operation known as divergence.
Divergence Definition
The divergence of a vector field F = (F1, F2, F3) in three-dimensional space is calculated using the formula:
∇·F = ∂F1/∂x + ∂F2/∂y + ∂F3/∂z
Where:
- F1, F2, and F3 are the components of the vector field along the x, y, and z axes respectively.
- ∂ denotes partial differentiation.
Components of the Electric Field
For the electric field E = i + j + k, we can identify the components as:
- F1 = 1 (coefficient of i)
- F2 = 1 (coefficient of j)
- F3 = 1 (coefficient of k)
Calculating the Divergence
Now we apply the divergence formula:
- ∂F1/∂x = ∂(1)/∂x = 0
- ∂F2/∂y = ∂(1)/∂y = 0
- ∂F3/∂z = ∂(1)/∂z = 0
Putting these together, we get:
∇·E = 0 + 0 + 0 = 0
Conclusion
The divergence of the electric field E = i + j + k is:
- The result is 0.
Therefore, the correct answer to the question is (c) 0.
|
Explore Courses for Physics exam
|
|
Similar Physics Doubts
If electric field hat E = i + j + k where i, j and k are the unit vectors in three-dimensions, the value of divergence of E is:(a)-3(b) 2(c) 0(d) 3?
Question Description
If electric field hat E = i + j + k where i, j and k are the unit vectors in three-dimensions, the value of divergence of E is:(a)-3(b) 2(c) 0(d) 3? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about If electric field hat E = i + j + k where i, j and k are the unit vectors in three-dimensions, the value of divergence of E is:(a)-3(b) 2(c) 0(d) 3? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If electric field hat E = i + j + k where i, j and k are the unit vectors in three-dimensions, the value of divergence of E is:(a)-3(b) 2(c) 0(d) 3?.
If electric field hat E = i + j + k where i, j and k are the unit vectors in three-dimensions, the value of divergence of E is:(a)-3(b) 2(c) 0(d) 3? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about If electric field hat E = i + j + k where i, j and k are the unit vectors in three-dimensions, the value of divergence of E is:(a)-3(b) 2(c) 0(d) 3? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If electric field hat E = i + j + k where i, j and k are the unit vectors in three-dimensions, the value of divergence of E is:(a)-3(b) 2(c) 0(d) 3?.
Solutions for If electric field hat E = i + j + k where i, j and k are the unit vectors in three-dimensions, the value of divergence of E is:(a)-3(b) 2(c) 0(d) 3? 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 If electric field hat E = i + j + k where i, j and k are the unit vectors in three-dimensions, the value of divergence of E is:(a)-3(b) 2(c) 0(d) 3? defined & explained in the simplest way possible. Besides giving the explanation of
If electric field hat E = i + j + k where i, j and k are the unit vectors in three-dimensions, the value of divergence of E is:(a)-3(b) 2(c) 0(d) 3?, a detailed solution for If electric field hat E = i + j + k where i, j and k are the unit vectors in three-dimensions, the value of divergence of E is:(a)-3(b) 2(c) 0(d) 3? has been provided alongside types of If electric field hat E = i + j + k where i, j and k are the unit vectors in three-dimensions, the value of divergence of E is:(a)-3(b) 2(c) 0(d) 3? theory, EduRev gives you an
ample number of questions to practice If electric field hat E = i + j + k where i, j and k are the unit vectors in three-dimensions, the value of divergence of E is:(a)-3(b) 2(c) 0(d) 3? 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
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup