Question

X
12. If the electric E field is given by (4î +3j +12k), calaulate the electric flux through
a surface area of 40 units lying in the y-z plane. (M.D.U. 2014) [Ans. 160 units]​

Answer 1

Answer:

Electric flux = 160 N/C units

Explanation:

Given:

• Electric field = 4i + 3j + 12k
• Surface area = 40 units (direction = yz plane)

To Find:

• Electric flux through the surface

Solution:

Here given that the surface area lies in the yz plane

Hence,

$\sf Surface\:area=40\: \hat{i}$

Now electric flux is given by the equation,

$\boxed{\sf Electric\:flux (\phi)=E.S}$

where E is the electric field and S is the area vector

Substituting the given data we get,

$\sf \phi = (4\hat{i}+3\hat{j}+12\hat{k}).(40\hat{i})$

$\sf \phi=(4 \times 40+3\times0+12\times 0)$

Solving it we get,

$\sf \phi=4\times40$

$\sf \implies \phi=160\: NC^{-1}\: units$

Hence the electric flux through the surface is 160 N/C units.

Answer 2

${\bf{Given\::}}$

• $\bf{\vec{E}\:=\:4\hat{i}\:+\:3\hat{j}\:+\:12\hat{k}\:}$

• Flux through a surface area of 40 units lying in the y-z plane.

$\\ {\bf{To\: Find\::}}$

• Electric flux.

$\\ {\bf{Solution\::}}$

✯ Area vector is defined as in the direction perpendicular to the plane in which the surface actually lies.

So,

➣ Here, in this case, the surface lies in the y-z plane.

Hence,

✯ Area vector would be defined in the plane perpendicular to y & z plane, i.e. x-plane.

$:\implies\:\bf{\vec{s}\:=\:40\hat{i}\:}$

As we know that,

$\orange\bigstar\:{\Large\mid}\:\bf\purple{Electric\:Flux\:(\phi)\:=\:\vec{E}\:.\:\vec{S}\:}\:{\Large\mid}\:\green\bigstar$

$\dashrightarrow\:\tt{\phi\:=\:\left(4\hat{i}\:+\:3\hat{j}\:+\:12\hat{k}\right)\:.\:(40\hat{i})\:}$

$\dashrightarrow\:\tt{\phi\:=\:4\hat{i}\times{40\hat{i}}\:+\:3\hat{j}\times{40\hat{i}}\:+\:12\hat{k}\times{40\hat{i}}\:}$

$\dashrightarrow\:\tt{\phi\:=\:160~(\hat{i}.\hat{i})\:+\:120~(\hat{j}.\hat{i})\:+\:480~(\hat{k}.\hat{i})\:}$

$\dashrightarrow\:\tt{\phi\:=\:160\times{1}\:+\:120\times{0}\:+\:480\times{0}\:}$

$\dashrightarrow\:\tt{\phi\:=\:160\:+\:0\:+\:0\:}$

$\dashrightarrow\:\bf\pink{\phi\:=\:160\:\dfrac{N}{C}.units}$