Question

Using Gauss’ Theorem calculate the flux of the vector field F ˆ
i ˆ
j kˆ = x + y + z r through
the surface of a cylinder of radius A and height H, which has its axis along the z-axis
and the base of the cylinder is on the xy-plane.

Answer 1

Answer:

Total flux due to given electric field is

$\phi = 3\pi r^2 H$

Explanation:

As we know that the flux through the closed surface is given as

$\phi = \int E. dA$

or we can also write it as

$\phi = \int div E. dV$

here we know that

$div E = (\frac{d}{dx}\hat i + \frac{d}{dy}\hat j + \frac{d}{dz}\hat k).E$

where we know that

$E = x\hat i + y \hat j + z\hat k$

so we have

$div E = 1 + 1 + 1 = 3$

now we have

$\phi = \int E. dV$

$\phi = 3 V$

$\phi = 3\pi r^2 H$

#Learn

Topic : Flux of electric field

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