Question

A disk with a radius of R is oriented with its normal unit vector at an angle Θ with respect to a uniform electric field. Which of the following represent the electric flux through the disk?

Answer 1

The expresion for the flux through the disk is:

Ф = E·πR^2·cos(Θ).

Step-by-step explanation:

Let's sat the electric field has direction e and the normal to the disk has direction n (bold means vector quantities). So we have:

E=E·e (where E is the magnitud of the electric flied)

A=A·n

The flux for an uniform electric field and a flat surface is:

Ф=E×A

⇒ Ф = E·A·e×n = E·A·cos(angle(e,n)) = E·A·cos(Θ)

Since in this case the area is for a disk of radius R,
`A=\pi R^(2)`

So, Ф = E·πR^2·cos(Θ)

Answer 2

The electric flux through the disk are

• E(πR²)sinϕ
• E(πR²)cosθ

Step-by-step explanation:

Electric Force is Calculated by:

Electric flux = E * A cosθ

where

E is the magnitude of the electric field

A represent area of the disk

and θ is the angle between the electric field lines and the normal (perpendicular) to A

Area, A = πR²

So, Electric flux = E(πR²) cosθ

Also, note that the cosine of an angle can be written as sine of its complementary angle.

Assuming θ + ϕ = 180

Then, cosθ = sinϕ

So, Electric flux = E(πR²) cosθ can be written as

Electric flux = E(πR²) sinϕ