Electric potential in a region is given by V=6x-8xy2-8y+6yz-4z2 The magnitude of electric force acting on a 2C charge placed at origin is (where x,y and z are in meter and V is in volt)

Question

Electric potential in a region is given by V=6x-8xy2-8y+6yz-4z2 The magnitude of electric force acting on a 2C charge placed at origin is (where x,y and z are in meter and V is in volt) (A) 2N (B) 20N (C) 6N (D) 8N

Tardigrade Admin · Accepted Answer

overset arrow Ex=-(d V/d x)=-[6 - 8 y2] hati overset arrow Ey=-(d V/d y)=-[.-16xy-8+6z]. hatj overset arrow Ez=-(d V/d y)=-[.6y-8z]. hatk at origin overset arrow E=-6 hati+8 hatj+0 hatk |. overset arrow E|.=10(N/C) F=qE=20N

Q. Electric potential in a region is given by $V = 6 x - 8 x y^{2} - 8 y + 6 yz - 4 z^{2}$ The magnitude of electric force acting on a $2 C$ charge placed at origin is (where $x, y$ and $z$ are in meter and $V$ is in volt)

$2 N$

$20 N$

$6 N$

$8 N$

$E \to_{x} = - \frac{d V}{d x} = - [6 - 8 y^{2}] \hat{i}$
$E \to_{y} = - \frac{d V}{d y} = - [- 16 x y - 8 + 6 z] \hat{j}$
$E \to_{z} = - \frac{d V}{d y} = - [6 y - 8 z] \hat{k}$
at origin $E \to = - 6 \hat{i} + 8 \hat{j} + 0 \hat{k}$
$∣ E \to ∣ = 10 \frac{N}{C}$
$F = qE = 20 N$

Q. Electric potential in a region is given by V=6x−8xy2−8y+6yz−4z2 The magnitude of electric force acting on a 2C charge placed at origin is (where x,y and z are in meter and V is in volt)

2N

20N

6N

8N