Question

If the electric potential at any point (x, y, z)m in space is given by V = 3x² volt. The electric field at the point (1, 0, 3)m will be ______.

Options

• 3Vm^-1, directed along the positive x-axis.

• 3Vm^-1, directed along the negative x-axis.

• 6Vm^-1, directed along the positive x-axis.

• 6Vm^-1, directed along the negative x-axis.

Answer 1

If the electric potential at any point (x, y, z)m in space is given by V = 3x² volt. The electric field at the point (1, 0, 3)m will be 6Vm^-1, directed along the negative x-axis.

Explanation:

The relation between electric field E and potential difference V is, E = `(-dV)/(dx)`

Hence, `vecE = (-dV)/(dx)I`

`vecE = -6xhati`

Hence, the electric field `vecE` at (1, 0, 3) is `vecE = 6hati` V/m.