In a region of space, the electric field is given by E⃗ =8iˆ+4jˆ+3kˆ. The electric flux through a surface of area of 100 units in x-y plane is

Question

In a region of space, the electric field is given by

$\mathbf{E} = 8 \hat{i} + 4 \hat{j} + 3 \hat{k}$ . The electric flux through a surface of area of 100 units in the x-y plane is

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Solution

The electric flux (Φ) through a surface is given by the dot product of the electric field (E) and the area vector (A). The area vector is perpendicular to the surface and its magnitude is equal to the area of the surface.

For a surface in the x-y plane, the area vector is along the z-axis. So, we can represent it as A = 0i + 0j + 100k.

Given, E = 8i + 4j + 3k.

The dot product of E and A is:

E.A = E_xA_x + E_yA_y + E_zA_z = 80 + 40 + 3100 = 0 + 0 + 300 = 300 units

So, the electric flux through the surface is 300 units.

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In a region of space, the electric field is given by E⃗ =8iˆ+4jˆ+3kˆ. The electric flux through a surface of area of 100 units in x-y plane is

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