A charge of 4 nC is placed uniformly on a square sheet of nonconducting material

Question

A charge of 4 nC is placed uniformly on a square sheet of nonconducting material of side 23 cm in the yz plane. (a) What is the surface charge density ? ________nC/m2 (b) What is the magnitude of the electric field to the right (x > 0) of the sheet _________kN/C To the left (x < 0) of the sheet? _________kN/C (c) The same charge is placed on a square conducting slab of side 23 cm and thickness 0.13 mm. What is the surface charge density ? Assume that the charge distributes itself uniformly on the large square surfaces. _________nC/m2 (d) What is the magnitude of the electric field to the right (x > 0) of the right face of the slab? _________kN/C To the left (x < 0) of the left face of the slab? _________kN/C

Explanation / Answer

charge Q = 4*10^-9 C
l = 0.23 m

The electric field of finite sheet E = s / 2 e_0
s = Q / l^2
s = 4*10^-9 / (0.23)^2 = 7.56*10^-8 C /m^2
e_0 = 8.85*10^-12 C^2 /N.m^2
electric field E = 7.56*10^-8 C /m^2 / 2*8.85*10^-12 C^2 /N.m^2 = 4271.19

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