The electric potential V at any point (x, y, z), all in metres in space is given by V = 4x2 volt. The electric field at the point (1, 0, 2) in volt/meter, is

Question

The electric potential V at any point (x, y, z), all in metres in space is given by V = 4x2 volt. The electric field at the point (1, 0, 2) in volt/meter, is (A) 8 along negative X-axis (B) 8 along positive X-axis (C) 16 along negative X-axis (D) 16 along positive X-axis

Tardigrade Admin · Accepted Answer

vec E =-[ hat i ( partial V / partial x )+ hat j ( partial V / partial y )+ hat k ( partial V / partial z )] vec E =-[ hat i (8 x )] vec E (1,0,2)=-8 hat i So electric field is 8 along negative x -axis.

Q. The electric potential $V$ at any point $(x, y, z)$ , all in metres in space is given by $V = 4 x^{2}$ volt. The electric field at the point $(1, 0, 2)$ in volt/meter, is

8 along negative X-axis

8 along positive X-axis

16 along negative X-axis

16 along positive X-axis

$E = - [\hat{i} \frac{\partial V}{\partial x} + \hat{j} \frac{\partial V}{\partial y} + \hat{k} \frac{\partial V}{\partial z}]$
$E = - [\hat{i} (8 x)]$
$E_{(1, 0, 2)} = - 8 \hat{i}$
So electric field is 8 along negative $x$ -axis.

Q. The electric potential V at any point (x,y,z), all in metres in space is given by V=4x2 volt. The electric field at the point (1,0,2) in volt/meter, is