Answer

Verified

429k+ views

**Hint:**To solve this question, we need to use the concept of Gauss Law for the electric flux. Using this concept, we can find the total charge by calculating the flux in the surface which will be a difference of the flux entering the surface and the flux leaving the surface.

**Formula Used:**The formula used in solving this question is given as

$\Rightarrow \oint {E.dl = \dfrac{{{Q_{enc}}}}{{{\varepsilon _0 }}}} $

Here, ${Q_{enc}}$ is the total charge enclosed within the surface, ${\varepsilon _0 }$ is the permittivity of free space, $E$ is the electric field and $\oint {E.dl} $ is the total flux in the surface.

**Complete step by step answer**

We know that Gauss law gives the total flux in the surface in terms of the total enclosed charge and permittivity of free space. Even though there are other ways of calculating total charge on the surface, since in the question we are given flux entering and leaving the surface so we should use Gauss Law to find the total enclosed charge.

Thus from Gauss Law, we know,

$\Rightarrow \oint {E.dl = \dfrac{{{Q_{enc}}}}{{{\varepsilon _0 }}}} $

But since, we are already given the flux entering and leaving the surface, we can calculate the total flux as,

$\Rightarrow \oint {E.dl = {\phi _2} - {\phi _1}} $

So, we can put this in the Gauss Law and get,

$

{\phi _2} - {\phi _1} = \dfrac{{{Q_{enc}}}}{{{\varepsilon _0 }}} \\

\Rightarrow {\varepsilon _0 }({\phi _2} - {\phi _1}) = {Q_{enc}} \\

$

Hence, we get the Total enclosed charge within the surface as ${\varepsilon _0 }({\phi _2} - {\phi _1})$

**$\therefore $Option (D) is correct out of the given options.**

**Note**

Always remember that Gauss Law can be used only in certain conditions. We should either be given the flux entering and leaving the surface as in this question or the surface given to us should have spherical, cylindrical or planar symmetry. If the question does not belong to any of the above two categories, then we should use other methods like Coulomb’s Law to calculate the total charge.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Mark and label the given geoinformation on the outline class 11 social science CBSE

When people say No pun intended what does that mea class 8 english CBSE

Name the states which share their boundary with Indias class 9 social science CBSE

Give an account of the Northern Plains of India class 9 social science CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE

Which are the Top 10 Largest Countries of the World?

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

How do you graph the function fx 4x class 9 maths CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths