Question

Question #a9813

Answer 1

`E=E_x=-12 V/m`

Explanation:

`"given: "V=3x^2`

`E_x=-(d V)/(d x)`

`E_y=0`

`E_z=0`

`E_x=-(d(3x^2))/(d x)`

`E_x=-6x`

`P=(color(green)(2),cancel(0),cancel(1))`

`E_x=-6*2`

`E_x=-12`

`E=E_x=-12 V/m`

Answer 2

`-12hatiV/m`

Explanation:

Potentoal at any point (x,y,z) ls
`V(x,y,z) =3x^2`
We know
#vecE=-(hati(deltaV)/(deltax)+hatj(deltaV)/(deltay)+hatk( deltaV)/(deltaz))#

The given function of Potential ‘V’ is independent of y and z.
So `( deltaV)/(deltay)=0 and ( deltaV)/(deltaz)=0`

`vecE=-hati(deltaV)/(deltax)`
`vecE=-(hatidelta(3x^2))/(deltax)`

`vecE=-hati(6x)`
At the given point `(2m,0,1m)`
the Electric field is(for x=2)

`vecE=-hati(6xx2)=-12hati V/m`
,if the umit of potential is Volt