The electric potential at a point (x , y , z) is given by: V=-x2y-xz3+4 The electric field overset arrow E at that point is:-

Question

The electric potential at a point (x , y , z) is given by: V=-x2y-xz3+4 The electric field overset arrow E at that point is:- (A)  overset arrow E= hati(2 x y - z3)+ hatjxy2+ hatk3z2x (B)  overset arrow E= hati(2 x y + z3)+ hatjx2+ hatk3xz2 (C)  overset arrow E= hati2xy+ hatj(x2 + y2)+ hatk(3 x z - y2) (D)  overset arrow E= hatiz3+ hatjxyz+ hatkz2

Tardigrade Admin · Accepted Answer

V=-x2y-xz3+4 Ex=(- partial V/ partial x)=-( partial (- x2 y - x z3 + 4)/ partial x)=+2xy+z3 Ey=(- partial V/ partial y)=-( partial (- x2 y - x z3 + 4)/ partial y)=+x2 Ez=(- partial V/ partial z)=-( partial (- x2 y - x z3 + 4)/ partial z)=+3xz2 so= overset arrow E=Ex hati+Ey hatj+Ez hatk

Q. The electric potential at a point $(x, y, z)$ is given by: $V = - x^{2} y - x z^{3} + 4$
The electric field $E \to$ at that point is:-

$E \to = \hat{i} (2 x y - z^{3}) + \hat{j} x y^{2} + \hat{k} 3 z^{2} x$

$E \to = \hat{i} (2 x y + z^{3}) + \hat{j} x^{2} + \hat{k} 3 x z^{2}$

$E \to = \hat{i} 2 x y + \hat{j} (x^{2} + y^{2}) + \hat{k} (3 x z - y^{2})$

$E \to = \hat{i} z^{3} + \hat{j} x yz + \hat{k} z^{2}$

Q. The electric potential at a point (x,y,z) is given by: V=−x2y−xz3+4 The electric field E→ at that point is:-

E→=i^(2xy−z3)+j^​xy2+k^3z2x

E→=i^(2xy+z3)+j^​x2+k^3xz2

E→=i^2xy+j^​(x2+y2)+k^(3xz−y2)

E→=i^z3+j^​xyz+k^z2

V=−x2y−xz3+4 Ex​=∂x−∂V​=−∂x∂(−x2y−xz3+4)​=+2xy+z3 Ey​=∂y−∂V​=−∂y∂(−x2y−xz3+4)​=+x2 Ez​=∂z−∂V​=−∂z∂(−x2y−xz3+4)​=+3xz2 so=E→=Ex​i^+Ey​j^​+Ez​k^

Q. The electric potential at a point $(x, y, z)$ is given by: $V = - x^{2} y - x z^{3} + 4$
The electric field $E \to$ at that point is:-

$E \to = \hat{i} (2 x y - z^{3}) + \hat{j} x y^{2} + \hat{k} 3 z^{2} x$

$E \to = \hat{i} (2 x y + z^{3}) + \hat{j} x^{2} + \hat{k} 3 x z^{2}$

$E \to = \hat{i} 2 x y + \hat{j} (x^{2} + y^{2}) + \hat{k} (3 x z - y^{2})$

$E \to = \hat{i} z^{3} + \hat{j} x yz + \hat{k} z^{2}$