Question

let us consider a uniform electric field 2i-8j+2k newton per coulamb what is the flux through a circle of area 5m square lying on x z plane​

Answer 1

ANSWER

Given:

• Electric Field(E) = (2i - 8j + 3k)N/C
• Area of circle (A) = 5m²
• Circle lies in x-z plane

To Find:

• Electric Flux(Φ)

Solution:

We are given that,

$:\implies\text{Electric Field}(\overrightarrow{E})=(2\hat{i}-8\hat{j}+3\hat{k})N/C$

Now, we are also given that,

$:\implies\text{Area of the circle(A)} =5m^2$

The circle lies on X-Z plane.

So, the Area vector points in Y Direction.

Hence,

$:\implies\text{Area vector}(\overrightarrow{A})=5\hat{j}$

Now, we know that,

$:\implies\text{Electric Flux = (Electric Field Vector)\cdot(Area Vector)}$

So,

$:\implies\phi=(\overrightarrow{E})\cdot(\overrightarrow{A})$

Therefore,

$:\implies\phi=(2\hat{i}-8\hat{j}+3\hat{k}))\cdot(5\hat{j})$

$:\implies\phi=(2\hat{i}\cdot5\hat{j})-(8\hat{j}\cdot5\hat{j})+(3\hat{k}\cdot5\hat{j})$

$:\implies\phi=10\hat{i}\cdot\hat{j}-40\hat{j}\cdot\hat{j}+15\hat{j}\cdot\hat{k}$

As,

⇒i•j = j•k = i•k= 0

And,

⇒i•i = j•j = k•k = 1

Hence,

$:\implies\phi=10(0)-40(1)+15(0)$

Therefore,

$:\implies\bf\phi=-40 V-m$

Therefore, the Electric Flux is -40 volt metres.

Concept Used:

1. Electric Field: It is defined as the electric force per unit charge.
2. Electric Flux: It is defined as rate of flow of the electric field through a given area.

Formulae Used:

• $\phi=(\overrightarrow{E})\cdot(\overrightarrow{A})$
• i•j = j•k = i•k= 0
• i•i = j•j = k•k = 1