Question

Write the expressions for the electric field strength due to several charges in terms of volume charge density, area charge density and linear charge density respectively

Answer 1

Let's write the expressions for the electric field strength due to several charges in terms of the following:

• Volume charge density

,

• Area charge density

,

• Linear Charge density

The electric field strength can be said to be expression which shows the intensity of an electric field at a given location.

Now, we have the following expressions:

• Electric field strength due to several charges in terms of volume.

We have the expression:

$E_P=\frac{1}{4\pi\epsilon0}\int_V(\frac{\rho dV}{r^2})r$

Where V is the volume, r is the distance between charges.

• Electric field strength in terms of area charge density:

We have the expression:

$E_p=\frac{1}{4\pi\epsilon0}\int_A(\frac{\sigma dA}{r^2})r$

Where A is the area and r is the distance between the charges.

• Electric field strength in terms of linear charge density:

$E_P=\frac{1}{4\pi\epsilon0}\int_l(\frac{\lambda dl}{r^2})r$

ANSWER:

• In terms of Volume charge density:

$\frac{1}{4\pi\epsilon0}\int_V(\frac{\rho dV}{r^2})r$

• In terms of area charge density:

$\frac{1}{4\pi\epsilon0}\int_A(\frac{\sigma dA}{r^2})r$

• In terms of linear charge density:

$\frac{1}{4\pi\epsilon0}\int_l(\frac{\lambda dl}{r^2})r$