Electric potential in volt (in region) is given by V=6x+8y+4z2 Calculate the electric force (in N ) acting on 2C point charge placed at origin.

Question

Electric potential in volt (in region) is given by V=6x+8y+4z2 Calculate the electric force (in N ) acting on 2C point charge placed at origin. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Ex=-( partial V/ partial x)=-6 hati Ey=-( partial v/ partial y)=-8 hatj Ez=-( partial V/ partial z)=-8z hatk overset arrow Enet at origin =√62 + 82=10 ⇒ | overset arrow F|=|q overset arrow E|=20N

Q. Electric potential in volt (in region) is given by
$V = 6 x + 8 y + 4 z^{2}$
Calculate the electric force (in $N$ ) acting on $2 C$ point charge placed at origin.

$E_{x} = - \frac{\partial V}{\partial x} = - 6 \hat{i}$
$E_{y} = - \frac{\partial v}{\partial y} = - 8 \hat{j}$
$E_{z} = - \frac{\partial V}{\partial z} = - 8 z \hat{k}$
$E \to_{n e t}$ at origin $= 6^{2} + 8^{2} = 10$
$\Rightarrow ∣ ∣ F \to ∣ ∣ = ∣ ∣ q E \to ∣ ∣ = 20 N$

Q. Electric potential in volt (in region) is given by V=6x+8y+4z2 Calculate the electric force (in N ) acting on 2C point charge placed at origin.

Ex​=−∂x∂V​=−6i^ Ey​=−∂y∂v​=−8j^​ Ez​=−∂z∂V​=−8zk^ E→net​ at origin =62+82​=10 ⇒∣∣​F→∣∣​=∣∣​qE→∣∣​=20N

Q. Electric potential in volt (in region) is given by
$V = 6 x + 8 y + 4 z^{2}$
Calculate the electric force (in $N$ ) acting on $2 C$ point charge placed at origin.

$E_{x} = - \frac{\partial V}{\partial x} = - 6 \hat{i}$
$E_{y} = - \frac{\partial v}{\partial y} = - 8 \hat{j}$
$E_{z} = - \frac{\partial V}{\partial z} = - 8 z \hat{k}$
$E \to_{n e t}$ at origin $= 6^{2} + 8^{2} = 10$
$\Rightarrow ∣ ∣ F \to ∣ ∣ = ∣ ∣ q E \to ∣ ∣ = 20 N$