Question #a9813

2 Answers
May 10, 2016

Answer:

#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#

May 12, 2016

Answer:

#-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 ā€˜Vā€™ 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