The figure shows a closed Gaussian surface in the shape of a cube of edge length
ID: 1283569 • Letter: T
Question
The figure shows a closed Gaussian surface in the shape of a cube of edge length 2.7 m, with one corner at x1= 4.4 m,y1= 4.3 m. The cube lies in a region where the electric field vector is given by E = -3.4i -4.2 y2j+3.0k N/C, with y in meters. What is the net charge (in Coulombs) contained by the cube?
The figure shows a closed Gaussian surface in the shape of a cube of edge length 2.7 m, with one corner at x1= 4.4 m,y1= 4.3 m. The cube lies in a region where the electric field vector is given by E = -3.4i -4.2 y^2j+3.0k N/C, with y in meters. What is the net charge (in Coulombs) contained by the cube?Explanation / Answer
length of the edge of the cube L = 2.5 m
distances x1 = 5 m and y1 = 3.7 m
electric field vector E = [-3.4 i^ - 4.4y2j^ + 2.8 k^] N/C
from Gauss's law ,
electric flux inside a closed surface is
? = ? E.dA ........................ (1)
non zero component of electric field is
Enon zero = - 4.4y2j^ N/C
the face of a cube located at y1 = 3.7 m has an area is
A = (2.5 m)(2.5 m)
= 6.25 m2
this area directed along +j^ direction.
the flux through the face is
? = Enon zero (A)
= (- 4.4y2 N/C)(6.25 m2)
= (- 4.4(3.7 m)2 N/C)(6.25 m2)
= -376.475 Wb
..................................................................................
the face of cube located at y = 3.7 m - 2.5 m = 1.2 m
this area directed along -j^ direction.
the flux through the face is
? = Enon zero (A)
= (- 4.4y2 N/C)(6.25 m2) cos180
= (- 4.4(1.2 m)2 N/C)(6.25 m2)(-1)
= 39.6 Wb
hence ,
the net electric flux is
? = -376.475 Wb + 39.6 Wb
= -336.875 Wb
using Gauss's law ,
charge Q = ?0?
= (8.85*10-12 C2/N.m2)(-336.875 Wb)
= -2.98*10-9 C
= -2.98 nC
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