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?

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 :

[tex]\phi=E{\cdot}A[/tex]

[tex]\phi=(4000j+3000k){\cdot}Ak[/tex]

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

[tex]\phi=3000\times Ak[/tex]

[tex]\phi=3000\times \pi (1.83)^2[/tex]

[tex]\phi=31562.63\ Nm^2/C[/tex]

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

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?

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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?