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Suppose electric potential varies along ...

Suppose electric potential varies along the x-axis as shown in the above figure the potential doesnot vary in `y or z` direction of the intervals shown (ignore the behaviour at the end points of the intervals) the field `E_(x)` has a maximum absolute value `"FB_(1)"Vm^(-1)` in the region `"FB_(2)"` its value in the region cd is `"FB_(3)"Vm^(-1)` then
The plot `E_(x)vsx` is

A

B

C

D

Text Solution

Verified by Experts

The correct Answer is:
D

`(E_(x))_(max)`Value `'FB_(1)'` in the region `FB_(2)`
`E_(x)`=value of `cd`is `FB_(3)Vm^(-1)`
`E=-(dV)/(dx)rArr E_(ab)=-((25)/(1))=-25`
`E_(be)=((5-15)/(1+2))=(10)/(3)E_(cd)=0`
`E_(de)=-((15-5)/(3-2))=-10`
`rArr (E_(x))_(Max)=25V//m^(-1)rArr FB_(2)` is `ab`
Taking the values of `E_(ab),E_(bc),E_(cd),E_(de),` .The plot of `E_(x)` Vsx will be as shown in `D` option.
For `a rarr b` part V` =25x+65`
`:.` when `V=0rArr x=(-65)/(25)=(-13)/(5)m`
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