Question

Consider the uniform electric field \vec{E} =(4000~\hat{j}+3000~\hat{k})~\text{N/C} ​E ​⃗ ​​ =(4000 ​j ​^ ​​ +3000 ​k ​^ ​​ ) N/C. What is its electric flux through a circular area of radius 1.83 m that lies in the xy-plane?

Answer 1

Answer:

Electric flux $\phi=31562.63\ Nm^2/C$

Explanation:

Given that,

Electric field acting on the circular area, $E=(4000j+3000k)\ N/C$

We need to find the electric flux through a circular area of radius 1.83 m that lies in the xy-plane. It lies in xy plane, such that the area vector point in z direction. The electric flux is given by :

$\phi=E{\cdot}A$

$\phi=(4000j+3000k){\cdot}Ak$

Using dot product properties, we get the value of electric flux as :

$\phi=3000\times Ak$

$\phi=3000\times \pi (1.83)^2$

$\phi=31562.63\ Nm^2/C$

So, the electric flux through a circular area is $\phi=31562.63\ Nm^2/C$ . Hence, this is the required solution.