Answer: a) 1.1115*10^-12 C, b) 3.53×10^-9 C/m²
Step-by-step explanation: according to gauss law, the electric flux from a gaussian surface is proportional to the magnitude of charge enclosed.
Mathematically, we have that
Electric flux = Q/ε0
But electric flux = EA
Hence we have that
EA = Q/ε0
Where E = strength of electric field = 4×10² N/c
A = Area of surface.
ε0 = permittivity of free space = 8.85×10^-12
Q = magnitude of charge enclosed by surface.
Let us find the area of the surface first, since diameter is 2cm, hence radius = diameter/2 = 2/2 = 1cm
Hence radius = 1cm = 0.01 m.
Since the surface is circular, area = πr²
Area (A) = 3.142×(0.01)² = 0.000314 m².
A)
Recall that
EA = Q/ε0
4×10² × 0.000314 = Q/8.85×10^-12
Q = 4×10² × 0.000314 × 8.85×10^-12
Q = 1.1115*10^-12 C
B)
Surface charge density = charge / Area
Surface charge density = 1.1115*10^-12/0.000315
Surface charge density = 3.53×10^-9 C/m²
