Assertion : If we plot potential versus x- coordinate graph along the x-axis, then field strength is zero where slope of `V -x` graph is zero.
Reason : If potential is function of x- only then
`E = - (dV)/(dx)`

Options

A. Both Assertion and Reason are true and the Reason is correct explanation of the Assertion.
B. Both Assertion and Reason are true but Reason is not the correct explantion of Assertion.
C. Assertion is true, but the Reason is false.
D. Assertion is false but the Reason is true.

Explanation

To solve the question, we need to analyze both the assertion and the reason provided.

### Step 1: Understand the Assertion
The assertion states that if we plot the potential \( V \) versus the x-coordinate graph along the x-axis, then the electric field strength \( E \) is zero where the slope of the \( V-x \) graph is zero.

### Step 2: Relate Electric Field and Potential
The electric field \( E \) is related to the electric potential \( V \) by the formula:
\[ E = -\frac{dV}{dx} \]
This means that the electric field is the negative rate of change of potential with respect to x. If the slope of the \( V-x \) graph is zero, then:
\[ \frac{dV}{dx} = 0 \]
This implies that:
\[ E = -0 = 0 \]
So, at points where the slope of the \( V-x \) graph is zero, the electric field strength \( E \) is indeed zero.

### Step 3: Analyze the Reason
The reason states that if the potential is a function of \( x \) only, then:
\[ E = -\frac{dV}{dx} \]
This is a correct statement. If the potential depends solely on \( x \), then the electric field can be defined as the negative gradient of the potential with respect to \( x \).

### Step 4: Conclusion
- The assertion is **true** because if the slope of the \( V-x \) graph is zero, the electric field strength is also zero.
- The reason is also **true** as it correctly describes the relationship between electric field and potential when potential is a function of \( x \) only.

### Final Answer
Both the assertion and the reason are true. However, the assertion's implication about the electric field being zero solely based on the slope being zero needs to be carefully considered in a multi-dimensional context.