Question

Potential difference between two points in a region having uniform electric field of $800\text{ N/C}$ is $16\text{V}$. Find the distance between two points.

Hint:

The standard SI unit for an Electric Field can be written as either $\text{N/C}$ or $\text{V/m}$.
Thinking of the unit specifically as $\text{V/m}$ serves as a great shortcut to remember the formula $E = \frac{V}{d}$.

Answer 1

Step 1: Understanding the Concept:
In a region with a perfectly uniform electric field, the potential difference between two distinct points along the field lines is directly proportional to the separation distance between them.
This is because the electric field represents the negative gradient of the electric potential.
Step 2: Key Formula or Approach:
The exact mathematical relationship between a uniform electric field $E$, the potential difference $\Delta V$, and the distance $d$ is given by $E = \frac{\Delta V}{d}$.
Rearranging this formula allows us to solve directly for the distance as $d = \frac{\Delta V}{E}$.
Step 3: Detailed Explanation:
The magnitude of the uniform electric field is $E = 800\text{ N/C}$.
The given potential difference between the points is $\Delta V = 16\text{ V}$.
Substituting these values into our rearranged equation:
\[ d = \frac{16}{800}\text{ m} \] \[ d = \frac{1}{50}\text{ m} \] \[ d = 0.02\text{ m} \] To express this distance more conveniently in centimeters, multiply the result by 100:
\[ d = 0.02 \times 100\text{ cm} = 2\text{ cm} \] Step 4: Final Answer:
The absolute distance between the two points is $2\text{ cm}$.