Question

The potential V is varying as V=1/2 ( y^2 - 4 x ) volt the field at coordinate ( 0 ,1 ) m will be

Answer 1

E = - dv/dr
E = - d[1/2(y^2 -4x)]/dr
E(x) = 4/2 = 2
E(y) = 2y/2 = y

E = 2i + yj
E = 2i + j volt/m

i hope it will help you
regards

Answer 2

Answer : Electric field is, E = 2i - j

Explanation :

Potential, $V=\dfrac{1}{2}(y^2-4x)$

We know that the relation between the electric field and the electric potential is :

$E=-[i\dfrac{\partial}{\partial x}+ j\dfrac{\partial}{\partial y}+ k\dfrac{\partial}{\partial z}]V$

$E=+2i-yj$

Electric field at at point (0,1)m will be :

$E=2i-j$

Hence, this is the required solution.