Question

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

• A. $1N/C$
• B. $5N/C$
• C. Zero
• D. $0.5N/C$

Answer 1

The correct option is C

Zero

Explanation for the correct option:

Step 1. Given data:

1. Volume $=0.2m^3$,
2. Electric potential $=5V$

Step 2. Formula used:

$E=-\frac{dV}{dx}$, Where $E=$Electric field, $dV=$Change in potential, $dx=$Change in distance,

Step 3. Explanation:

1. The space surrounding a charged particle is associated with a field known as an electric field.
2. The total amount of work that an external agent must do in moving a particle of unit charge from infinity to the point in an electric field where potential has to be determined, is called electric potential. Electric potential is denoted by $V$.
3. We know that $E=-\frac{dV}{dx}$, where $V$ and $x$ are the potential and distance.
4. If $V$ = constant, then $E=0$. It is clear that if the electric potential is constant, then the electric field will be zero. We know that derivative of a constant is zero.
5. Since, potential is constant throughout, $dV=0$, for any displacement dr. Hence, electric field in this region is zero.
6. So, the magnitude of the electric field in this region is zero.

Hence option (C) is correct.