Two plates, one at 300 V, other at - 100 V are 4 cm apart. The voltage at 3 cm from the second plate is:

Options

A. 250 V
B. 500 V
C. 200 V
D. 400 V

Explanation

To find the voltage at a point between two plates, we can follow these steps:

### Step 1: Identify the given values
- Voltage of the first plate (V1) = 300 V
- Voltage of the second plate (V2) = -100 V
- Distance between the plates (d) = 4 cm
- Distance from the second plate where we need to find the voltage (x) = 3 cm

### Step 2: Calculate the potential difference (ΔV) between the two plates
The potential difference (ΔV) is given by:
\[ \Delta V = V1 - V2 = 300 V - (-100 V) = 300 V + 100 V = 400 V \]

### Step 3: Determine the electric field (E) between the plates
The electric field (E) between the plates can be calculated using the formula:
\[ E = \frac{\Delta V}{d} \]
Substituting the values:
\[ E = \frac{400 V}{4 cm} = \frac{400 V}{0.04 m} = 10000 \, \text{V/m} \]

### Step 4: Calculate the voltage at the point 3 cm from the second plate
To find the voltage at a point that is 3 cm from the second plate, we can use the formula:
\[ V = V2 + E \cdot x \]
Where:
- \(V2\) is the voltage of the second plate (-100 V)
- \(E\) is the electric field (10000 V/m)
- \(x\) is the distance from the second plate (3 cm = 0.03 m)

Substituting the values:
\[ V = -100 V + (10000 \, \text{V/m}) \cdot (0.03 m) \]
\[ V = -100 V + 300 V = 200 V \]

### Step 5: Conclusion
The voltage at 3 cm from the second plate is **200 V**.

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