Electric Flux Density

To determine the electric flux through a surface area in the presence of an electric field, we use the concept of the dot product between the electric field vector and the area vector. The formula for electric flux ( ) is:

Where:

• is the electric field vector
• is the area vector. The direction of is perpendicular to the surface.

In this problem, the electric field vector is:

The surface area is given as , and since it lies in the YZ-plane, the area vector is perpendicular to this plane. The direction of indicates that the area vector is:

The dot product is calculated as follows:

Using the properties of the dot product, where only the components in the same direction ( ) will contribute to the product, this simplifies to:

Therefore, the electric flux through the surface is 180 Nm²/C.

This matches with the given correct answer option: 180.

To calculate the electric flux, we use the formula: Φ = E ⋅ A, where Φ is the electric flux, E is the electric field, and A is the area vector, defined as the product of the magnitude of the area and the unit normal vector to the surface. Given the provided vectors:
Electric field,
Unit normal vector,
We express the area vector as:
A = 4 = .
Now, we find the dot product:
E ⋅ A =
=
=
= .
Hence, the electric flux is 12 . This value falls within the specified range of 12 to 12.