Question

Explain the measurement of electric flux with examples.

Answer 1

Measuring electric flux:

1. Electric flux refers to the total number of electric field lines passing through a given area in a unit time.
2. The electric flux can be calculated using the formula, ${\Phi }_E=E.A=EA\cos \theta$ (where $E$ = electric field, $A$= area of surface and $\theta$= angle between electric field lines and perpendicular to $A$)
3. If the plane is normal to the given electric field, the formula becomes, ${\Phi }_E=EA$.

Example 1: A plane surface has an area of $2m^2$. If an electric field of magnitude $3V/m$ crosses it at an angle of ${60}^o$, calculate the electric flux.

Solution:

${\Phi }_E=E.A=EA\cos \theta$

${\Phi }_E=3\times 2\times \cos {60}^o=3\times 2\times \frac{1}{2}$

${\Phi }_E=3Vm$

Example 2: Consider a planar disc of radius $12cm$making an angle of ${30}^o$with a uniform electric field as shown in the figure. The electric field is $\stackrel{\rightharpoonup }{E}=300\hat{i}V/m$. What is the amount of electric flux passing through it?

Solution:

Area, $A={\mathrm{\pi R}}^2=\mathrm{\pi }\times 0.12\times 0.12=0.045{\mathrm{m}}^2$

$\theta ={60}^o$, $E=300V/m$

${\Phi }_E=E.A=EA\cos \theta$

${\Phi }_E=300\times 0.045\times \cos {60}^o=6.75Vm$