Consider the uniform electric field \vec{E} =(4000~\hat{j}+3000~\hat{k})~\text{N/C} E ⃗ =(4000 j ^ +3000 k ^ ) N/

Question

WITCHER

3 months ago

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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?

Physics

1 answer:

kicyunya [3.2K] · Answer 1 · 2026-03-04T01:54:31+03:00

Answer:

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

Explanation:

We start with the given parameters:

The electric field impacting the circular surface is $E=(4000j+3000k)\ N/C$

Our objective is to ascertain the electric flux passing through a circular region with a radius of 1.83 m situated in the xy-plane. The area vector is oriented in the z direction. The formula for electric flux is expressed as:

$\phi=E{\cdot}A$

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

Applying properties of the dot product, we calculate the electric flux as:

$\phi=3000\times Ak$

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

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

Consequently, the electric flux for the circular area is $\phi=31562.63\ Nm^2/C$ . Thus, this represents the required answer.

Consider the uniform electric field \vec{E} =(4000~\hat{j}+3000~\hat{k})~\text{N/C} ​E ​⃗ ​​ =(4000 ​j ​^ ​​ +3000 ​k ​^ ​​ ) N/

Consider the uniform electric field \vec{E} =(4000~\hat{j}+3000~\hat{k})~\text{N/C} E ⃗ =(4000 j ^ +3000 k ^ ) N/