Two plates are at potentials `-10 V` and `+30 V`. If the separation between the plates be `2 cm`. The electric filed between them is

Options

A. 2000 V/m
B. 1000 V/m
C. 500 V/m
D. 3000 V/m

Answer

To find the electric field between two plates with given potentials, we can follow these steps:

### Step 1: Identify the potentials and separation
We have two plates with potentials:
- \( V_1 = -10 \, \text{V} \) (potential of the first plate)
- \( V_2 = +30 \, \text{V} \) (potential of the second plate)

The separation between the plates is given as:
- \( D = 2 \, \text{cm} = 2 \times 10^{-2} \, \text{m} \)

### Step 2: Use the formula for electric field
The electric field \( E \) between two plates is given by the formula:
\[ E = \frac{\Delta V}{D} \]
where \( \Delta V = V_2 - V_1 \).

### Step 3: Calculate \( \Delta V \)
Substituting the values of \( V_1 \) and \( V_2 \):
\[ \Delta V = V_2 - V_1 = 30 \, \text{V} - (-10 \, \text{V}) = 30 \, \text{V} + 10 \, \text{V} = 40 \, \text{V} \]

### Step 4: Substitute \( \Delta V \) and \( D \) into the electric field formula
Now, substituting \( \Delta V \) and \( D \) into the electric field formula:
\[ E = \frac{40 \, \text{V}}{2 \times 10^{-2} \, \text{m}} = \frac{40}{0.02} \, \text{V/m} \]

### Step 5: Calculate the electric field
Calculating the above expression:
\[ E = \frac{40}{0.02} = 2000 \, \text{V/m} \]

### Final Answer
The electric field between the plates is \( E = 2000 \, \text{V/m} \).

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