Question

How will the electric field vary according to point (x, y, z), if the electric potential at any point (x, y, z) is given by V = 3x2. 
1. 6x
2. -6x
3. 3x
4. -3x²

Answer 1

Correct Answer - Option 2 : -6x

CONCEPT:

• Electric Potential: An electric potential is the amount of work that is needed to move a unit charge in an electric field from a reference point to a specific point without producing an acceleration.
• The relation between the electric field (E) and Electric potential (V): Electric field is the gradient of electric potential (V) in the x-direction.

\(E = {-dV \over dx}\)

CALCULATION:

Given that V = 3x2

\(E = {-dV \over dx}= {-d(3x^2) \over dx}=-6x\)

So the correct answer is option 2.