Answer
405k+ views
Hint:Find whether the given surface is Gaussian surface or not. If it is a Gaussian surface apply the gauss formula and substitute the number of faces that it encloses to find the electric flux that comes out of each face of the given closed surface.
Useful formula:
The Gaussian law is given as
$f = \dfrac{Q}{{{ \in _0}}}$
Where $f$ is the total electric flux, $Q$ is the charge enclosed by the surface and ${ \in _0}$ is the permittivity of the free space.
Complete step by step solution:
It is given that the charge of $ + Q$ is placed at the centre of the box. The Gauss’s law provides the information about the distribution of the electric charges for the closed surface. In the closed surface, the electric flux is directly proportional to the electric charges enclosed in the surface.
In the given question, the cubical surface encloses the charge $ + Q$ . Since the cube is the closed surface with the six faces, the gauss law can be applied to find the electric flux of it.
By using the formula of the Gaussian law,
$f = \dfrac{Q}{{{ \in _0}}}$
Since the cube contains the six faces, the permittivity of the free space is multiplied by six to find the flux from each face.
$f = \dfrac{Q}{{6{ \in _0}}}$
Hence the electric flux that is coming out of each flux is obtained as $\dfrac{Q}{{6{ \in _0}}}$
Thus the option (D) is correct.
Note:The Gauss law is used for the determination of electric field over the closed surface and the charge distribution in it. Remember that if the charge $Q$ is placed outside of the cube, there will be no electric flux on the closed surface. Hence the charge on the surface alone can contribute to the electric flux.
Useful formula:
The Gaussian law is given as
$f = \dfrac{Q}{{{ \in _0}}}$
Where $f$ is the total electric flux, $Q$ is the charge enclosed by the surface and ${ \in _0}$ is the permittivity of the free space.
Complete step by step solution:
It is given that the charge of $ + Q$ is placed at the centre of the box. The Gauss’s law provides the information about the distribution of the electric charges for the closed surface. In the closed surface, the electric flux is directly proportional to the electric charges enclosed in the surface.
![seo images](https://www.vedantu.com/question-sets/57bd8eaa-5b30-4230-be86-72eaf9dbecc22035249146177978993.png)
In the given question, the cubical surface encloses the charge $ + Q$ . Since the cube is the closed surface with the six faces, the gauss law can be applied to find the electric flux of it.
By using the formula of the Gaussian law,
$f = \dfrac{Q}{{{ \in _0}}}$
Since the cube contains the six faces, the permittivity of the free space is multiplied by six to find the flux from each face.
$f = \dfrac{Q}{{6{ \in _0}}}$
Hence the electric flux that is coming out of each flux is obtained as $\dfrac{Q}{{6{ \in _0}}}$
Thus the option (D) is correct.
Note:The Gauss law is used for the determination of electric field over the closed surface and the charge distribution in it. Remember that if the charge $Q$ is placed outside of the cube, there will be no electric flux on the closed surface. Hence the charge on the surface alone can contribute to the electric flux.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)