WRONG PROBLEM OF HC VERMA

·         WRONG PROBLEM OF H C VERMA

H C Verma  (Part 2)  Gauss’s Law   Page # 141        Problem # 4

Q. The electric field in a region is given by E = (E_ox/L) i . Find the charge contained inside a cubical volume bounded by the surfaces x = 0, x = a, y = 0, y = a, z = 0, z = a. Take E_o = 5 ×10³ N/C, L = 2 cm and a = 1 cm.  

SOLUTION:

NOTE: This question has conceptual mistake.

•  As electric field is given by the eqn. E = (E_ox/L) i , it means electric field is towards positive x-axis right of y-z axis and it is towards –ve x axis  left of y-z axis. 
• It means field lines are parallel.
• Parallel field lines mean that field is uniform.
• But as field depends on value of x, it can’t be uniform.
• Hence, there is a contradiction.

• Figure explanation.
• Plane x = 0 corresponds to y-z plane , shown by left face in the figure.
• Plane x = a corresponds to y-z plane , shown by right face in the figure.
• Plane y = 0 corresponds to x-z plane , shown by bottom face in the figure.
• Plane y = a corresponds to x-z plane , shown by top face in the figure.
• Plane z = 0 corresponds to x-y plane , shown by back face in the figure.
• Plane z = a corresponds to x-y plane , shown by front face in the figure.