Electric potential in space V(x , y , z)=(x2 + y2 + z2)V . If the magnitude of electric field strength E at (1 m , 0 m , 2 m) in NC- 1 is 4.47× 10n then find n :

Question

Electric potential in space V(x , y , z)=(x2 + y2 + z2)V . If the magnitude of electric field strength E at (1 m , 0 m , 2 m) in NC- 1 is 4.47× 10n then find n : (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

E =-(( partial V / partial x )+( partial V / partial y ) hat j +( partial V / partial z ) hat k ) =-(2 x hat i +2 y hat j +2 z hat k ) E =-(2 hat i +0 hat j +4 hat k ) E =√20=2 √5=4.47 N C -1=4.47 × 100 N C -1

Q. Electric potential in space $V (x, y, z) = (x^{2} + y^{2} + z^{2}) V$ . If the magnitude of electric field strength E at $(1 m, 0 m, 2 m)$ in $N C^{- 1}$ is $4.47 \times 1 0^{n}$ then find $n$ :

$E = - (\frac{\partial V}{\partial x} + \frac{\partial V}{\partial y} \hat{j} + \frac{\partial V}{\partial z} \hat{k})$
$= - (2 x \hat{i} + 2 y \hat{j} + 2 z \hat{k})$
$E = - (2 \hat{i} + 0 \hat{j} + 4 \hat{k})$
$E = 20 = 25 = 4.47 N C^{- 1} = 4.47 \times 1 0^{0} N C^{- 1}$

Q. Electric potential in space V(x,y,z)=(x2+y2+z2)V . If the magnitude of electric field strength E at (1m,0m,2m) in NC−1 is 4.47×10n then find n :

E=−(∂x∂V​+∂y∂V​j^​+∂z∂V​k^) =−(2xi^+2yj^​+2zk^) E=−(2i^+0j^​+4k^) E=20​=25​=4.47NC−1=4.47×100NC−1

Q. Electric potential in space $V (x, y, z) = (x^{2} + y^{2} + z^{2}) V$ . If the magnitude of electric field strength E at $(1 m, 0 m, 2 m)$ in $N C^{- 1}$ is $4.47 \times 1 0^{n}$ then find $n$ :

$E = - (\frac{\partial V}{\partial x} + \frac{\partial V}{\partial y} \hat{j} + \frac{\partial V}{\partial z} \hat{k})$
$= - (2 x \hat{i} + 2 y \hat{j} + 2 z \hat{k})$
$E = - (2 \hat{i} + 0 \hat{j} + 4 \hat{k})$
$E = 20 = 25 = 4.47 N C^{- 1} = 4.47 \times 1 0^{0} N C^{- 1}$