The electric potential V at any point (x, y, z) in space is given by V = 3x2 where x, y, z are all in metre. The electric field at the point (1 m, 0, 2 m) is

Question

The electric potential V at any point (x, y, z) in space is given by V = 3x2 where x, y, z are all in metre. The electric field at the point (1 m, 0, 2 m) is (A) 6 V m-1 along negative x-axis (B) 6 V m-1 along positive x-axis (C) 12 V m-1 along negative x-axis (D) 12 V m-1 along positive x-axis

Tardigrade Admin · Accepted Answer

Electric potential V=3 x2 E=-(d V/d x) E=(d/d x)(3 x3) E=-6 x At the point (1,0,2) Electric field E=6 × 1=-6 V / m

Q. The electric potential V at any point $(x, y, z)$ in space is given by $V = 3 x^{2}$ where $x, y, z$ are all in metre. The electric field at the point (1 m, 0, 2 m) is

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

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

$12 V m^{- 1}$ along negative $x$ -axis

$12 V m^{- 1}$ along positive $x$ -axis

$8 V m^{- 1}$ along negative $x$ -axis

Electric potential $V = 3 x^{2}$
$E = - \frac{d V}{d x}$
$E = \frac{d}{d x} (3 x^{3})$
$E = - 6 x$
At the point $(1, 0, 2)$
Electric field $E = 6 \times 1 = - 6 V / m$

Q. The electric potential V at any point (x,y,z) in space is given by V=3x2 where x,y,z are all in metre. The electric field at the point (1 m, 0, 2 m) is

6Vm−1 along negative x-axis

6Vm−1 along positive x-axis

12Vm−1 along negative x-axis

12Vm−1 along positive x-axis

8Vm−1 along negative x-axis

Electric potential V=3x2 E=−dxdV​ E=dxd​(3x3) E=−6x At the point (1,0,2) Electric field E=6×1=−6V/m