The electric potential Vat a point P(x,y,z) in space is given by `V = 4x^(2)V`. Find the electric field at a point (1 m, 0, 2 m) in V/m.

Explanation

Given, potential, `V = 4x^(2)`
Now, x-component of electric field is
`E_(x) = -(dV)/(dx)`
`rArr E_(x) = -d/(dx) (4x^(2))`
`rArr E_( x) = - 8x`
y-component of electric field is
`E_(y) = -(dV)/(dy)`
`rArr E_(Y) = -d/(dy) (4x^(2))`
z-component of electric field is
`E_(z) = -(dV)/(dz)`
`therefore` Electric field,
`E =E_(x) hati +E_(y)hatj + E_(z)hatk`
`rArr E = -8xhati + 0 + 0`
`rArr E =-8xhati`
`therefore` At point (1 m, 0, 2 m) the electric field is
`E = -8 xx (1) hati rArr E = -8hati N//C`