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  4. In a region of space, the electric field is given by <math><mover accent=true><mrow><mi>E</mi></mrow><mo>→</mo></mover><mo>=</mo><mn>8</mn><mover accent=true><mrow><mover accent=true><mrow><mi mathvariant=normal>i</mi></mrow></mover></mrow><mo></mo></mover><mo>+</mo><mn>4</mn><mover accent=true><mrow><mover accent=true><mrow><mi mathvariant=normal>j</mi></mrow></mover></mrow><mo></mo></mover><mo>+</mo><mn>3</mn><mover accent=true><mrow><mi>k</mi></mrow><mo></mo></mover><mo>.</mo></math> The electric flux through a surface of area of 100 units in <math><mi>x</mi></math>-<math><mi>y</mi></math> plane is

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Q. In a region of space, the electric field is given by E→=8i^+4j^+3k^. The electric flux through a surface of area of 100 units in x-y plane is

NTA AbhyasNTA Abhyas 2022

Solution:

Here,  E→=8i^+4j^+3k^ 
S→=100k^
(direction of the area is perpendicular to x-y plane)
ϕ=E→⋅ S→=8i^+4j^+3k^ ⋅100k^ 
= 300 units