Question

The electric flux through a square-shaped area of side 6 cm near a large charged sheet is found to be 5 ✕ 10−5 N · m2/C when the area is parallel to the plate. Find the charge density on the sheet (in C/m2). (Enter the magnitude.)

Answer 1

Answer:

$\sigma =2.363\times 10^{-13}C/m^{2}$

Explanation:

Given that,

Side of sheet = 6cm

Electric Flux = $5\times10^{-5}N.m^2/C$

Area of the square sheet, A= 6×6

= 36cm²

= 36×10⁻⁴ m²

Now

the electric flux (Φ) is given as:

$\phi =EA$

where, E = Electric field

substituting the values in the  equation,

$E=\frac{5\times10^{-5}N.m^2/C}{36\times 10^{-4}}\\E=0.0139N/C$

Now the charge density (σ) on a sheet is given as:

$\sigma=2\epsilon_oE$

where, = Permittivity of the free space = 8.85×10⁻¹²

substituting the values in the above equation, we get

$\sigma=2\times 8.85\times10^{-12}\times 0.0139\\\\\sigma=2.363\times 10^{-13}C/m^{2}$