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
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
Updated On: Jul 29, 2022
- 8 along negative X-axis
- 8 along positive X-axis
- 16 along negative X-axis
- 16 along positive X-axis
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The Correct Option is A
Solution and Explanation
$\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.
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Concepts Used:
Electric Field
Electric Field is the electric force experienced by a unit charge.
The electric force is calculated using the coulomb's law, whose formula is:
\(F=k\dfrac{|q_{1}q_{2}|}{r^{2}}\)
While substituting q2 as 1, electric field becomes:
\(E=k\dfrac{|q_{1}|}{r^{2}}\)
SI unit of Electric Field is V/m (Volt per meter).