Question

Figure 21.61 shows disk shaped region of radius of 2 cm on which there is a uniform electric field of magnitude 300 V/m at an angle of 30⁰ to the plane of the disk. Assume that points upward in +y direction. Calculate the electric flux on the disk, and include the correct units.

Short answer

The electric flux for plane is $0.33V.m$.

Step-by-step solution

Identification of given data

The radius of disk shaped region is$r=2cm$

The magnitude of uniform electric field is $E=300V/m$.

The angle of electric field with plane of disk is$\theta =30°$ .

Conceptual Explanation

The electric flux is calculated by the product of magnitude of electric field with the horizontal component of the surface area of disk.

Determination of electric flux of the disk

The surface area of the disk is given as:

$A=\pi r^2$

Substitute all the values in the above equation.

$$\begin{gathered} A=\pi {\left[\left(2\text{cm}\right)\left(\frac{1\text{m}}{100\text{cm}}\right)\right]}^2 \\ A=1.26\times {10}^{-3}{\text{m}}^2 \end{gathered}$$

The electric flux for plane is given as:

$\varphi =EA\cos \theta$

Substitute all the values in the above equation.

$$\begin{gathered} \varphi =\left(300\text{V}/\text{m}\right)\left(1.26\times {10}^{-3}{\text{m}}^2\right)\left(\cos 30°\right) \\ \varphi =0.33\text{V}·\text{m} \end{gathered}$$

Therefore, the electric flux for plane is $0.33V.m$.