The electric potential as a function of is given by The electric field at a point (2, 3) m is

Question

The electric potential as a function of $x, y$ is given by $V = 5 (x^{2} - y^{2}) V .$ The electric field at a point (2, 3) m is _____ V/m. [2026]

Smart Achievers · Accepted Answer

(1)

$V = 5 (x^{2} - y^{2}) V$

$V = 5 x^{2} - 5 y^{2}, E_{x} = - \frac{\partial V}{\partial x} = - 10 x \hat{i}$

$x = 2, y = 3, E_{y} = - \frac{\partial V}{\partial y} = + 10 y \hat{j}$

$\vec{E} = (- 20 \hat{i} + 30 \hat{j}) N/C$

Solution

Q.
The electric potential as a function of $x, y$ is given by $V = 5 (x^{2} - y^{2}) V .$ The electric field at a point (2, 3) m is _____ V/m. [2026]

1 $(- 20 \hat{i} + 30 \hat{j})$

2 $(20 \hat{i} - 30 \hat{j})$

3 $(20 \hat{i} + 45 \hat{j})$

4 $(- 4 \hat{i} + 6 \hat{j})$

Ans.
(1)

$V = 5 (x^{2} - y^{2}) V$

$V = 5 x^{2} - 5 y^{2}, E_{x} = - \frac{\partial V}{\partial x} = - 10 x \hat{i}$

$x = 2, y = 3, E_{y} = - \frac{\partial V}{\partial y} = + 10 y \hat{j}$

$\vec{E} = (- 20 \hat{i} + 30 \hat{j}) N/C$

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Solution

Q. The electric potential as a function of x, y is given by V=5(x2-y2) V. The electric field at a point (2, 3) m is _____ V/m. [2026]

1 (-20i^+30j^)

2 (20i^-30j^)

3 (20i^+45j^)

4 (-4i^+6j^)

Ans. (1) V=5(x2-y2) V V=5x2-5y2, Ex=-∂V∂x=-10xi^ x=2, y=3, Ey=-∂V∂y=+10yj^ E→=(-20i^+30j^) N/C