Question

The electrostatic potential is given as a function of x in figure (a) and (b). Calculate the corresponding electric fields in regions A, B, C and D. Plot the electric field as a function of x for figure (b).

1. 
   
2. 
   

Answer 1

Figure a:

`vec"E" = - "dv"/"dx" hat"i"`

From 0 to 0.2 m,

`"E"_"x" = "dv"/"dx" = 3/0.2 = 30/2 = 15`Vm^-1 (region A)

`"E"_"x" = "dv"/"dx"` = 0 

Since the potential is constant (region B)

`"E"_"x" = "dv"/"dx" = (-2)/0.2 = (-20)/2` = - 10 Vm^-1 (region c) 

`"E"_"x" = "dv"/"dx" = 6/0.2 = 60/2` = 30 Vm^-1 (region d)

Figure b:

`"E"_"x" = "dv"/"dx"` = - 30 Vm^-1 (region 0-1 cm)

`"E"_"x" = "dv"/"dx"` = 30 Vm^-1 (region 1-2 cm)

`"E"_"x" = "dv"/"dx"` = 0   (region 2-3 cm)

`"E"_"x" = "dv"/"dx"` = 30 Vm^-1 (region 3-4 cm)

`"E"_"x" = "dv"/"dx"` = - 30 Vm^-1 (region 4-5 cm)