Question

The electric potential $V$ at any point $(x, y, z)$, all in metres in space is given by $V = 4x^2$ volt. The electric field at the point $(1, 0, 2)$ in volt/meter, is

• A. 8 along negative X-axis
• B. 8 along positive X-axis
• C. 16 along negative X-axis
• D. 16 along positive X-axis

Answer 1

Answer: (A)

8 along negative X-axis

Answer 2

$\vec{ E }=-\left[\hat{ i } \frac{\partial V }{\partial x }+\hat{ j } \frac{\partial V }{\partial y }+\hat{ k } \frac{\partial V }{\partial z }\right]$ $\vec{ E }=-[\hat{ i }(8 x )]$ $\vec{ E }_{(1,0,2)}=-8 \hat{ i }$ So electric field is 8 along negative $x$ -axis.