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21.An electric field vec E=alphahat i betahat j gammahat k exists in space where alpha beta gamma are constants.Magnitude of electric flux per unit area through a plane surface ax by cz=d is (a b cand d are constants) (a) (a alpha b beta cr)/(sqrt(a^(2) b^(2) c^(2))) (b) (a alpha b beta c gamma)/(a b c) (c) (sqrt(a^(2)alpha^(2) b^(2)beta^(2) c^(2)gamma^(2)))/(sqrt(a^(2) b^(2) gamma^(2))) (d) alpha beta gamma?
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21.An electric field vec E=alphahat i betahat j gammahat k exists in s...
Electric Flux and Electric Field
Electric flux is a measure of the electric field passing through a given area. It is defined as the dot product of the electric field vector and the area vector. Mathematically, the electric flux (Φ) through a surface is given by:
Φ = ∫∫ E · dA
Where E is the electric field vector and dA is an infinitesimal area vector. The dot product of E and dA gives the component of the electric field that is perpendicular to the area vector.
Electric Flux through a Plane Surface
In this problem, we are given an electric field vector E = αĥi + βĥj + γĥk, where α, β, and γ are constants. We need to find the magnitude of the electric flux per unit area through a plane surface defined by the equation ax + by + cz = d, where a, b, c, and d are constants.
To find the electric flux, we need to calculate the dot product of the electric field vector and the area vector of the plane surface. The area vector of the plane surface can be determined by taking the gradient of the equation of the plane.
The equation of the plane is ax + by + cz = d. Taking the gradient of this equation gives us the normal vector to the plane, which is also the area vector:
∇(ax + by + cz) = aĥi + bĥj + cĥk
Therefore, the area vector of the plane is aĥi + bĥj + cĥk.
Calculating the Dot Product
Now, we can calculate the dot product of the electric field vector and the area vector:
E · A = (αĥi + βĥj + γĥk) · (aĥi + bĥj + cĥk)
= αa + βb + γc
Therefore, the magnitude of the electric flux per unit area through the plane surface is |E · A| = |αa + βb + γc|.
Final Answer
The magnitude of the electric flux per unit area through the plane surface ax + by + cz = d is |αa + βb + γc|. Thus, the correct option is (d) αβγ.
Electric flux is a measure of the electric field passing through a given area. It is defined as the dot product of the electric field vector and the area vector. Mathematically, the electric flux (Φ) through a surface is given by:
Φ = ∫∫ E · dA
Where E is the electric field vector and dA is an infinitesimal area vector. The dot product of E and dA gives the component of the electric field that is perpendicular to the area vector.
Electric Flux through a Plane Surface
In this problem, we are given an electric field vector E = αĥi + βĥj + γĥk, where α, β, and γ are constants. We need to find the magnitude of the electric flux per unit area through a plane surface defined by the equation ax + by + cz = d, where a, b, c, and d are constants.
To find the electric flux, we need to calculate the dot product of the electric field vector and the area vector of the plane surface. The area vector of the plane surface can be determined by taking the gradient of the equation of the plane.
The equation of the plane is ax + by + cz = d. Taking the gradient of this equation gives us the normal vector to the plane, which is also the area vector:
∇(ax + by + cz) = aĥi + bĥj + cĥk
Therefore, the area vector of the plane is aĥi + bĥj + cĥk.
Calculating the Dot Product
Now, we can calculate the dot product of the electric field vector and the area vector:
E · A = (αĥi + βĥj + γĥk) · (aĥi + bĥj + cĥk)
= αa + βb + γc
Therefore, the magnitude of the electric flux per unit area through the plane surface is |E · A| = |αa + βb + γc|.
Final Answer
The magnitude of the electric flux per unit area through the plane surface ax + by + cz = d is |αa + βb + γc|. Thus, the correct option is (d) αβγ.
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21.An electric field vec E=alphahat i betahat j gammahat k exists in space where alpha beta gamma are constants.Magnitude of electric flux per unit area through a plane surface ax by cz=d is (a b cand d are constants) (a) (a alpha b beta cr)/(sqrt(a^(2) b^(2) c^(2))) (b) (a alpha b beta c gamma)/(a b c) (c) (sqrt(a^(2)alpha^(2) b^(2)beta^(2) c^(2)gamma^(2)))/(sqrt(a^(2) b^(2) gamma^(2))) (d) alpha beta gamma?
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21.An electric field vec E=alphahat i betahat j gammahat k exists in space where alpha beta gamma are constants.Magnitude of electric flux per unit area through a plane surface ax by cz=d is (a b cand d are constants) (a) (a alpha b beta cr)/(sqrt(a^(2) b^(2) c^(2))) (b) (a alpha b beta c gamma)/(a b c) (c) (sqrt(a^(2)alpha^(2) b^(2)beta^(2) c^(2)gamma^(2)))/(sqrt(a^(2) b^(2) gamma^(2))) (d) alpha beta gamma? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about 21.An electric field vec E=alphahat i betahat j gammahat k exists in space where alpha beta gamma are constants.Magnitude of electric flux per unit area through a plane surface ax by cz=d is (a b cand d are constants) (a) (a alpha b beta cr)/(sqrt(a^(2) b^(2) c^(2))) (b) (a alpha b beta c gamma)/(a b c) (c) (sqrt(a^(2)alpha^(2) b^(2)beta^(2) c^(2)gamma^(2)))/(sqrt(a^(2) b^(2) gamma^(2))) (d) alpha beta gamma? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 21.An electric field vec E=alphahat i betahat j gammahat k exists in space where alpha beta gamma are constants.Magnitude of electric flux per unit area through a plane surface ax by cz=d is (a b cand d are constants) (a) (a alpha b beta cr)/(sqrt(a^(2) b^(2) c^(2))) (b) (a alpha b beta c gamma)/(a b c) (c) (sqrt(a^(2)alpha^(2) b^(2)beta^(2) c^(2)gamma^(2)))/(sqrt(a^(2) b^(2) gamma^(2))) (d) alpha beta gamma?.
21.An electric field vec E=alphahat i betahat j gammahat k exists in space where alpha beta gamma are constants.Magnitude of electric flux per unit area through a plane surface ax by cz=d is (a b cand d are constants) (a) (a alpha b beta cr)/(sqrt(a^(2) b^(2) c^(2))) (b) (a alpha b beta c gamma)/(a b c) (c) (sqrt(a^(2)alpha^(2) b^(2)beta^(2) c^(2)gamma^(2)))/(sqrt(a^(2) b^(2) gamma^(2))) (d) alpha beta gamma? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about 21.An electric field vec E=alphahat i betahat j gammahat k exists in space where alpha beta gamma are constants.Magnitude of electric flux per unit area through a plane surface ax by cz=d is (a b cand d are constants) (a) (a alpha b beta cr)/(sqrt(a^(2) b^(2) c^(2))) (b) (a alpha b beta c gamma)/(a b c) (c) (sqrt(a^(2)alpha^(2) b^(2)beta^(2) c^(2)gamma^(2)))/(sqrt(a^(2) b^(2) gamma^(2))) (d) alpha beta gamma? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 21.An electric field vec E=alphahat i betahat j gammahat k exists in space where alpha beta gamma are constants.Magnitude of electric flux per unit area through a plane surface ax by cz=d is (a b cand d are constants) (a) (a alpha b beta cr)/(sqrt(a^(2) b^(2) c^(2))) (b) (a alpha b beta c gamma)/(a b c) (c) (sqrt(a^(2)alpha^(2) b^(2)beta^(2) c^(2)gamma^(2)))/(sqrt(a^(2) b^(2) gamma^(2))) (d) alpha beta gamma?.
Solutions for 21.An electric field vec E=alphahat i betahat j gammahat k exists in space where alpha beta gamma are constants.Magnitude of electric flux per unit area through a plane surface ax by cz=d is (a b cand d are constants) (a) (a alpha b beta cr)/(sqrt(a^(2) b^(2) c^(2))) (b) (a alpha b beta c gamma)/(a b c) (c) (sqrt(a^(2)alpha^(2) b^(2)beta^(2) c^(2)gamma^(2)))/(sqrt(a^(2) b^(2) gamma^(2))) (d) alpha beta gamma? in English & in Hindi are available as part of our courses for Physics.
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