Question

If the electric potential at any point $( x , y , z ) m$ in space is given by $V =3 x ^{2}$ volt. The electric field at the point $(1,0,3) m$ will be :

• A. $3\, Vm ^{-1}$, directed along positive $x$-axis.
• B. $3\,Vm ^{-1}$, directed along negative $x$-axis.
• C. $6\, Vm ^{-1}$, directed along positive $x$-axis.
• D. $6\, Vm ^{-1}$, directed along negative $x$-axis.

Answer 1

Answer: (D)

$E _{ x }=-\frac{\partial V }{\partial x }=-6 x$
At $(1,0,3)$
$\vec{ E }=-6 V / m \hat{ i }$