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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.
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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?
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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?.
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