Question

In a certain region of space with volume $0.2 \,m^3$, the electric potential is found to be $5\,V$ throughout. The magnitude of electric field in this region is:

• A. zero
• B. 0.5 N/C
• C. 1 N/C
• D. 5 N/C

Answer 1

The Correct Option is A

The problem involves determining the magnitude of the electric field in a region where the electric potential is constant. Let's analyze the situation step-by-step:

1. We are given that the electric potential $V$ throughout the region is $5\,V$ and the volume of the region is $0.2 \,m^3$.
2. The relationship between electric potential $V$ and electric field $E$ is given by the gradient equation: E = -\nabla V. This equation states that the electric field is the negative gradient of the electric potential.
3. In this specific case, since the electric potential is constant throughout the region, the gradient of $V$ is zero. Mathematically: \nabla V = 0
4. Therefore, the electric field, which is the negative of this gradient, is also zero: E = -0 = 0.

Thus, the magnitude of the electric field in the given region is zero.

Hence, the correct answer is: zero.