Question

The electric potential V at any point (x, y, z) is given by V = 3x² where x is in metres and V in volts. The electric field at the point (1 m, 0, 2 m) is ______.

Options

• 6 V/m along −x-axis

• 6 V/m along +x-axis

• 1.5 V/m along −x-axis

• 1.5 V/m along +x-axis

Answer 1

The electric potential V at any point (x, y, z) is given by V = 3x² where x is in metres and V in volts. The electric field at the point (1 m, 0, 2 m) is 6 V/m along −x-axis.

Explanation:

`E = (- dV)/dx`

or, `E = -d/dx (3x^2)`

∴ E = −6x

 Putting x = l ,

E = 6 V/m along −x-axis.