Question

The electric field in a region of space is given by $E=5\hat{i}+2\hat{j}N/C$. The flux of $E$ due to this field through an area $1m^2$ lying in the $y-z$ plane, in SI units is?

Answer 1

Step 1: Given Data

The electric field is $E=5\hat{i}+2\hat{j}N/C$

The area of the region is $A=1m^2$

The area is lying in $y-z$ plane

Step 2: Formula used

Magnetic flux $\Phi =BA\cos \theta$

Where $B$ is the magnetic field

$A$ is the area

$\theta$ is the angle between the magnetic field and the area vector

Step 3: Finding the electric field that passes through the given area

1. Given that the area is lying in $y-z$ plane, that implies the electric field through $y$ and $z$ planes induce zero magnetic flux as they will be parallel to the area.
2. Only the magnetic field through $x$ axis has to be included in the calculation of magnetic flux as it is perpendicular to the $y-z$ plane or the angle between the magnetic field and the area vector is zero degrees.
3. ⇒ The magnetic field $B=5N/C$ that has to be included in the calculation.

Step 4: The calculation

$$\begin{gathered} \Phi =BA\cos \left(\theta \right) \\ \Phi =\left(5\right)\left(1\right)\cos \left(0^{\circ }\right) \\ \Phi =5N{m}^2/C \end{gathered}$$

Thus, the magnetic flux passing through the given area is $5N{m}^2/C$.