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 :

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.

Tardigrade Admin · Accepted Answer

E x =-( partial V / partial x )=-6 x At (1,0,3) vec E =-6 V / m hat i

Q. 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 :

$3 V m^{- 1}$ , directed along positive $x$ -axis.

$3 V m^{- 1}$ , directed along negative $x$ -axis.

$6 V m^{- 1}$ , directed along positive $x$ -axis.

$6 V m^{- 1}$ , directed along negative $x$ -axis.

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

Q. If the electric potential at any point (x,y,z)m in space is given by V=3x2 volt. The electric field at the point (1,0,3)m will be :

3Vm−1, directed along positive x-axis.

3Vm−1, directed along negative x-axis.

6Vm−1, directed along positive x-axis.

6Vm−1, directed along negative x-axis.