Question

The electric potential for an electric field directed parallel to the X-axis is shown in the figure. Choose the correct plot of electric field strength.

• A.

  

• B.

  

• C.

  

• D.

  

Answer 1

The Correct Option is A

Given: A graph of electric potential \( V \) along the X-axis. We are to choose the correct graph of

electric field strength \( E \). Key Concept: Electric field is the negative gradient (slope) of electric potential: \[ E = -\frac{dV}{dx} \] - Where the potential decreases linearly, \( E \) is constant and negative. - Where the slope of \( V(x) \) increases, \( E \) becomes more negative. - Where the slope becomes less steep (towards flat), \( E \) approaches zero. - If slope changes sign, \( E \) changes sign. 

Analyzing the given potential graph: - From left to right, the slope (negative of \( E \)) is: - Steep (large negative) - Moderate (less negative) - Flat (zero) - Positive slope (negative \( E \)), so field becomes positive So, \( E \) starts negative, increases toward zero, then becomes positive. 

Correct Plot: The electric field graph that starts negative, increases, crosses zero, and becomes positive.