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If the electric potential at any point x , y , z m in space is given by V = 3 x 2 volt. The electric field at the point 1 , 0 , 3 m will be :

Options

  1. A3   Vm - 1 , directed along positive x -axis.
  2. B3   Vm - 1 , directed along negative x -axis.
  3. C6   Vm - 1 , directed along negative x -axis.
  4. D6   Vm - 1 , directed along positive x -axis.

Correct answer

C. 6   Vm - 1 , directed along negative x -axis.

Step-by-step solution

Electric potential V = 3 x 2 Electric potential and electric field are related as E = - d V d x = - 6 x . 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.

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