If the electric potential at any point x ,   y ,   z   m in space is given by V = 3 x 2 volt.…

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 :
  1. 3 Vm-1, directed along positive x-axis.
  2. 3 Vm-1, directed along negative x-axis.
  3. 6 Vm-1, directed along negative x-axis.
  4. 6 Vm-1, directed along positive x-axis.

Solution

Electric potential V=3x2

Electric potential and electric field are related as E=-dVdx=-6x.

At the point 1, 0, 3 m, 

⇒E=-6×1=-6 V m-1

Thus, electric field is 6 V m-1 along negative x‐ axis.

Asked in: JEE Main 2022 (29 Jun Shift 2)

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