Question

The electric potential V at any point x, y, z (all in meters) in space is given by `V=4x^2` volts. The electric field at the point (1m, 0, 2m) is……………..`V//m`.

Answer 1

As electric field `E` is related to potential `V` through the relation
`E=-(dV)/(dr)`
`E_(x)=-(dV)/(dx)=-(d)/(dx)(4x^(2))=-8x`
`E_(y)=(dV)/(dt)=-(d)/(dy)(4x^(2))=0`
and `E_(z)=-(dV)/(dt)=-(d)/(dz)(4x^(2))=0`
So `vec(E)=hat(i)E_(x)+hat(j)E_(y)+hat(k)E_(z)=-8xhat(i)` ltbr. i.e, it has magnitude `8V//m` and is directed along negative `x-axis`