Question

Electric field in the region is given by \( \vec{E} = \left(\dfrac{M}{x^3}\right)\hat{i}\). The correct expression for the potential in the region is [assume potential at infinity is zero]:

• A. \(\dfrac{M}{2x^2}\)
• B. \(Mx^2\)
• C. \(\dfrac{M}{3x^4}\)
• D. \(\dfrac{M}{x^2}\)

Hint:

Electric potential is obtained by integrating electric field with a negative sign.

Answer 1

The Correct Option is A

Step 1: Relation between electric field and potential: \[ E = -\frac{dV}{dx} \]
Step 2: \[ -\frac{dV}{dx} = \frac{M}{x^3} \Rightarrow dV = -M x^{-3} dx \]
Step 3: \[ V = \frac{M}{2x^2} \] (using \(V(\infty)=0\))