The potential of the electric field produced by a point charge at any point (x, y, z) is given by V= 3x2 + 5 , where x, y, z are in metres and V is in volts. The intensity of the electric field at (-2,1,0) is

Question

The potential of the electric field produced by a point charge at any point (x, y, z) is given by V= 3x2 + 5 , where x, y, z are in metres and V is in volts. The intensity of the electric field at (-2,1,0) is (A) +17 V m-1 (B) -17 V m-1 (C) +12 v m-1 (D) -12 V m-1

Tardigrade Admin · Accepted Answer

Potential ( V )=3 x 2+5 Intensity of the electric field, E=(-d V/d x) ∴ E =-( d (3 x 2+5)/ dx )=-6 x .∴ E | x =-2=-6(-2)=12 V / m

Q. The potential of the electric field produced by a point charge at any point $(x, y, z)$ is given by $V = 3 x^{2} + 5$ , where $x, y, z$ are in metres and $V$ is in volts. The intensity of the electric field at $(- 2, 1, 0)$ is

$+ 17 V m^{- 1}$

$- 17 V m^{- 1}$

$+ 12 v m^{- 1}$

$- 12 V m^{- 1}$

Potential $(V) = 3 x^{2} + 5$
Intensity of the electric field, $E = \frac{- d V}{d x}$
$∴ E = - \frac{d ( 3 x ^{2} + 5 )}{d x} = - 6 x$
$∴ E ∣_{x = - 2} = - 6 (- 2) = 12 V / m$

Q. The potential of the electric field produced by a point charge at any point (x,y,z) is given by V=3x2+5 , where x,y,z are in metres and V is in volts. The intensity of the electric field at (−2,1,0) is

+17Vm−1

−17Vm−1

+12vm−1

−12Vm−1