Question

Let V be the electric potential at a given point. Then the electric field $ {{E}_{x}} $ along $ x- $ direction at that point is given by

• A. $ \int_{0}^{\infty }{V}dx $
• B. $ \frac{dV}{dx} $
• C. $ -\frac{dV}{dx} $
• D. $ -V\frac{dV}{dx} $

Answer 1

Answer: (C)

The electric Held intensity at a point in an electric field in a given direction is equal to he negative potential gradient in that direction ie, $ E=-\frac{dV}{dx} $ The negative sign signifies that the potential decreases in the direction of the electric field. Note: It is evident from above relation, that the electric field E can also be expressed in the unit volt / metre or $ V{{m}^{-1}} $ Thus, $ 1\,N{{C}^{-1}}=1\,V{{m}^{-1}} $