Question

How much electric flux will come out through a surface $S = 10\hat{j} $ kept in an electrostatic field $\mathop E\limits^ \to = 2\hat{i} + 4\hat{j} + 7\hat{k} $
A. $20$ units
B. $40$ units
C. $70$ units
D. Nearly $80$ units

Answer 1

Hint: In the given question, electric flux is coming throughout our surface which is kept at an electrostatic force field. By using above information and electric flux formula we are going to calculate how many electric flux units are coming out. For this we use the electric flux formula.

Complete step by step answer:
Electric flux is proportional to the number of electric field lines given in the virtual surface.Electric flux is the rate of flow of electric charge through some given area.
Given surface, $S = 10\hat{j} $
And electric field, $\mathop E\limits^ \to = 2\hat{i} + 4\hat{j} + 7\hat{k} $
By using electric flux formula, $\phi = \mathop E\limits^ \to .S$
By substituting the values of surface and electric field in the above formula we get,
$\phi = \left( {2\hat{i} + 4\hat{j} + 7\hat{k} } \right)\left( {10\hat{j} } \right)$
In the above equation we are neglecting the values of $\hat{i}$ and $\hat{j} $ so that,
Electric flux, $\phi = 4\hat{j} \times 10\hat{j} $
Here the $\hat{j} $ value becomes $1$ so the value of electric flux is,
$\phi = 40$ units
The electric flux coming out of the surface is $40$ units.

Hence, the correct option is B.

Note: From the given data and using the electric flux formula we have derived the given question. In the above solution part we have neglected the $\hat{i}$ and $\hat{k} $ because the surface of the flux is given in $\hat{j} $ so that we have neglected those values and calculated only $\hat{j} $ value.