From the following graph, find the value of `( vec(E ))` at `r = 3.5`

Options

A. `3.5 V //m`
B. ` infty`
C. `(100)/(35)V//m`
D. Zero

Answer

To find the value of the electric field \( \vec{E} \) at \( r = 3.5 \) m from the given graph, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Relationship**: The electric field \( \vec{E} \) is related to the electric potential \( V \) by the equation:
\[ \vec{E} = -\frac{dV}{dr} \]
This means that the electric field is the negative rate of change of the electric potential with respect to the distance \( r \).

2. **Identify the Given Value**: We are given \( r = 3.5 \) m and need to find \( \vec{E} \) at this point.

3. **Analyze the Graph**: Since the problem states that we should refer to a graph of voltage versus \( r \), we need to look at the slope of the graph at \( r = 3.5 \) m.

4. **Determine the Slope**: If the graph shows that the voltage \( V \) is constant at \( r = 3.5 \) m, then the change in voltage \( dV \) with respect to \( dr \) will be zero. This can be interpreted as:
\[ \frac{dV}{dr} = 0 \]

5. **Calculate the Electric Field**: Substituting this result into the equation for the electric field:
\[ \vec{E} = -\frac{dV}{dr} = -0 = 0 \]

6. **Conclusion**: Therefore, the value of the electric field \( \vec{E} \) at \( r = 3.5 \) m is:
\[ \vec{E} = 0 \]

### Final Answer:
The value of \( \vec{E} \) at \( r = 3.5 \) m is \( 0 \).

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