The electric potential at a space point P (x , y , z) is given as V=x2+y2+z2 . The modulus of the electric field at that point is proportional to

Question

The electric potential at a space point P (x , y , z) is given as V=x2+y2+z2 . The modulus of the electric field at that point is proportional to (A) V(1/2) (B) V (C) V(3/2) (D) V2

Tardigrade Admin · Accepted Answer

Ex=-2x, Ey=-2 and Ez=-2z |E|=√Ex2 + Ey2 + Ez2 =√4 x2 + 4 y2 + 4 z2 =2√x2 + y2 + z2=2√V

Q. The electric potential at a space point $P (x, y, z)$ is given as $V = x^{2} + y^{2} + z^{2}$ . The modulus of the electric field at that point is proportional to

$V^{\frac{1}{2}}$

$V$

$V^{\frac{3}{2}}$

$V^{2}$

$E_{x} = - 2 x, E_{y} = - 2$ and $E_{z} = - 2 z$
$∣ E ∣ = E_{x}^{2} + E_{y}^{2} + E_{z}^{2}$
$= 4 x^{2} + 4 y^{2} + 4 z^{2}$
$= 2 x^{2} + y^{2} + z^{2} = 2 V$

Q. The electric potential at a space point P(x,y,z) is given as V=x2+y2+z2 . The modulus of the electric field at that point is proportional to

V21​

V

V23​

V2

Ex​=−2x,Ey​=−2 and Ez​=−2z ∣E∣=Ex2​+Ey2​+Ez2​​ =4x2+4y2+4z2​ =2x2+y2+z2​=2V​

Q. The electric potential at a space point $P (x, y, z)$ is given as $V = x^{2} + y^{2} + z^{2}$ . The modulus of the electric field at that point is proportional to

$V^{\frac{1}{2}}$

$V$

$V^{\frac{3}{2}}$

$V^{2}$

$E_{x} = - 2 x, E_{y} = - 2$ and $E_{z} = - 2 z$
$∣ E ∣ = E_{x}^{2} + E_{y}^{2} + E_{z}^{2}$
$= 4 x^{2} + 4 y^{2} + 4 z^{2}$
$= 2 x^{2} + y^{2} + z^{2} = 2 V$