Question

Assume that the electric field \(\vec{E}=30x^{2}\hat{i}\) exists in space. Then the potential difference \(V_{A}-V_{O}\), where '\(V_{O}\)' is the potential at the origin and '\(V_{A}\)' is the potential at \(x=2\) m, is

• A. \(-120\) V
• B. \(80\) V
• C. \(120\) V
• D. \(-80\) V

Hint:

Potential difference is the negative integral of the field along x.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept
\(V_A-V_O=-\int_0^{2}E\,dx\)

Step 2: Integrate
\(\int_0^{2}30x^{2}dx=30\times\dfrac{x^{3}}{3}\Big|_0^{2}=10\times8=80\)

Step 3: Result
\(V_A-V_O=-80\) V

Final Answer:
The potential difference is minus 80 V. \[ \boxed{\text{(D) }-80\ \text{V}} \]