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A of radius 'R' is placed in a uniform field E. where hat E =(3 i -2 j 4 k ) N/C The net electric flux through the sphere?
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A of radius 'R' is placed in a uniform field E. where hat E =(3 i -2 j...
Calculating Electric Flux through a Sphere in a Uniform Electric Field
Given:
Electric Flux:
Electric flux is the measure of how much electric field passes through a given surface. It is calculated by multiplying the electric field by the area of the surface and then taking the dot product of the two vectors.
Calculating Electric Flux through a Sphere:
To calculate the electric flux through a sphere, we need to use Gauss's law, which states that the electric flux through a closed surface is proportional to the charge enclosed within that surface. For a sphere, the charge enclosed is given by:
q = 4πε₀R²E
where ε₀ is the permittivity of free space.
The electric flux through a sphere is given by:
Φ = E.A
where A is the area of the sphere.
Substituting the value of q, we get:
Φ = 4πε₀R²E.A
Calculating Area of a Sphere:
The area of a sphere is given by:
A = 4πR²
Substituting the value of A, we get:
Φ = 4πε₀R²E.4πR²
Simplifying the expression, we get:
Φ = 16π²ε₀R⁴E
Final Answer:
The net electric flux through the sphere is given by:
Φ = 16π²ε₀R⁴E
Note:
Make sure to use the correct units while calculating the electric flux. The SI unit of electric flux is Nm²/C.
Given:
- Radius of sphere, R
- Uniform electric field, E = (3i - 2j + 4k) N/C
Electric Flux:
Electric flux is the measure of how much electric field passes through a given surface. It is calculated by multiplying the electric field by the area of the surface and then taking the dot product of the two vectors.
Calculating Electric Flux through a Sphere:
To calculate the electric flux through a sphere, we need to use Gauss's law, which states that the electric flux through a closed surface is proportional to the charge enclosed within that surface. For a sphere, the charge enclosed is given by:
q = 4πε₀R²E
where ε₀ is the permittivity of free space.
The electric flux through a sphere is given by:
Φ = E.A
where A is the area of the sphere.
Substituting the value of q, we get:
Φ = 4πε₀R²E.A
Calculating Area of a Sphere:
The area of a sphere is given by:
A = 4πR²
Substituting the value of A, we get:
Φ = 4πε₀R²E.4πR²
Simplifying the expression, we get:
Φ = 16π²ε₀R⁴E
Final Answer:
The net electric flux through the sphere is given by:
Φ = 16π²ε₀R⁴E
Note:
Make sure to use the correct units while calculating the electric flux. The SI unit of electric flux is Nm²/C.
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A of radius 'R' is placed in a uniform field E. where hat E =(3 i -2 j 4 k ) N/C The net electric flux through the sphere?
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A of radius 'R' is placed in a uniform field E. where hat E =(3 i -2 j 4 k ) N/C The net electric flux through the sphere? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A of radius 'R' is placed in a uniform field E. where hat E =(3 i -2 j 4 k ) N/C The net electric flux through the sphere? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A of radius 'R' is placed in a uniform field E. where hat E =(3 i -2 j 4 k ) N/C The net electric flux through the sphere?.
A of radius 'R' is placed in a uniform field E. where hat E =(3 i -2 j 4 k ) N/C The net electric flux through the sphere? for NEET 2025 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A of radius 'R' is placed in a uniform field E. where hat E =(3 i -2 j 4 k ) N/C The net electric flux through the sphere? covers all topics & solutions for NEET 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A of radius 'R' is placed in a uniform field E. where hat E =(3 i -2 j 4 k ) N/C The net electric flux through the sphere?.
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