Question

The electric potential V at any point $(x, y, z)$ in space is given by $V = 3x^{2}$ where $x, y, z$ are all in metre. The electric field at the point (1 m, 0, 2 m) is

• A. $6 \,V\, m^{-1}$ along negative $x$-axis
• B. $6 \,V \,m^{-1}$ along positive $x$-axis
• C. $12\, V\, m^{-1}$ along negative $x$-axis
• D. $12\, V \,m^{-1}$ along positive $x$-axis
• E. $8\, V\,m^{-1}$ along negative $x$-axis

Answer 1

Answer: (A)

Electric potential $V=3 x^{2}$
$E=-\frac{d V}{d x}$
$E=\frac{d}{d x}\left(3 x^{3}\right) $
$E=-6 x $
At the point $(1,0,2)$
Electric field $E=6 \times 1=-6 V / m$