Eight solid plastic cubes, each 2.8 cm on each edge, are glued together to form

Question

Eight solid plastic cubes, each 2.8 cm on each edge, are glued together to form each one of the objects(i, ii, iii, and iv) shown in the figure below.
(a) Assuming each object carries charge with uniform density of 400 nC/m^3 throughout its volume, find the charge of each object.
(b) Assuming each object carries charge with uniform density 20.0 nC/m^2 everywhere on its exposed surface, find the charge on each object.
(i)
(ii)
(iii)
(iv)

Assuming charge is placed only on the edges where perpendicular surfaces meet, with a uniform density 100.0 pC/m, find the charge of each object.
(i) )  
(ii)  
(iii)  
(iv)  

Explanation / Answer

part A :

Volume of each cube V = 8 times of side^3

V = 8 * 0.028^3

V = 0.000175 m^3

charge of each cube Q = rho * V

Q = 400 e-9 * 0.000175

Q = 700 nC

----------------------------------------------------------

part B :

area A = 0.028 * 0.028 = 0.000784 m^2

(i) for 6*4 = 24 squares

Charge Q = sigma * A = (20 e-9 )*24*(0.000784) = 3.76 *10^-10 C

(ii) 34 squares

Charge Q = sigma * A = (20 e-9 )*34 * (0.000784) = 5.33 *10^-10 C

(iii) 34 squares

Charge Q = sigma * A = (20 e-9 )*34 * (0.000784) = 5.33 *10^-10 C

(iv) 32 squares

Charge Q = sigma * A = (20 e-9 )*32 * (0.000784) = 5.01 *10^-11 C
----------------------------------------------------

part C:

(i) total edge length l = 24 * 0.028 = 0.672 m

Q = Lambda * L = 100 e-12 * 0.672 = 6.72 *10^-11 C

(ii) total length = 44 * 0.028 = 1.23 m

charge Q = 100 e-12 * 1.23 = 1.23 *10^-10 C

(iii) total length L = 64 * 0.028 = 1.792 m

charge Q = 100 e -12 * 1.792 = 1.792 *10^10 C

(iv) L = 40 * 0.028 = 1.12 m

charge Q = 1.12 * 100 e-12 = 1.12 e -10 C

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