The potential gradient along the length of a uniform wire is 20 volt/metre. B and C are the two points at 40 cm and 70 cm point on a meter scale fitted along the wire. What is the potential difference between B and C?

Options

A. 6V
B. 0.4 V
C. 0.6 V
D. 4 V

Explanation

To find the potential difference between points B and C on a uniform wire, we can follow these steps:

### Step 1: Understand the given information
We know that the potential gradient (V/g) along the wire is 20 volts per meter. This means that for every meter of length, the potential changes by 20 volts.

### Step 2: Identify the positions of points B and C
Point B is located at 40 cm (0.4 m) and point C is located at 70 cm (0.7 m) on the meter scale.

### Step 3: Calculate the distance between points B and C
To find the distance between points B and C, we subtract the position of B from the position of C:
\[ \text{Distance (d)} = \text{Position of C} - \text{Position of B} \]
\[ d = 0.7 \, \text{m} - 0.4 \, \text{m} = 0.3 \, \text{m} \]

### Step 4: Use the formula for potential difference
The potential difference (V) between two points in a uniform electric field can be calculated using the formula:
\[ V = \text{Potential Gradient} \times \text{Distance} \]
Substituting the values we have:
\[ V = 20 \, \text{V/m} \times 0.3 \, \text{m} \]

### Step 5: Calculate the potential difference
Now, we perform the multiplication:
\[ V = 20 \times 0.3 = 6 \, \text{V} \]

### Conclusion
The potential difference between points B and C is 6 volts.

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