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

Answer 1

Answer: (A)

$6 \,V\, m^{-1}$ along negative $x$-axis

Answer 2

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 $E=6 \times 1=-6 V / m$