Refer to above question , the potential difference between C and D is :

Options

A. 80 m V
B. zero
C. 40 mV
D. 60 mV

Answer

To find the potential difference between points C and D, we can follow these steps:

### Step 1: Identify the given values
- Side of the square (length of the rod) = 20 cm = 0.2 m
- Rate of change of magnetic field (dB/dt) = 2 T/s

### Step 2: Determine the induced electric field (E)
The induced electric field (E) due to the changing magnetic field is given by the formula:
\[ E = \frac{d}{2} \cdot \frac{dB}{dt} \]
where \( d \) is the distance from the center of the square to the side where points C and D are located. Since the side length is 20 cm, the distance \( d \) is:
\[ d = 20 \, \text{cm} = 0.2 \, \text{m} \]

Substituting the values:
\[ E = \frac{0.2}{2} \cdot 2 = 0.1 \cdot 2 = 0.2 \, \text{V/m} \]

### Step 3: Calculate the potential difference (V) between points C and D
The potential difference (V) can be calculated using the formula:
\[ V = E \cdot L \]
where \( L \) is the length of the rod between points C and D, which is also 20 cm = 0.2 m.

Substituting the values:
\[ V = 0.2 \cdot 0.2 = 0.04 \, \text{V} \]

### Step 4: Convert the potential difference to millivolts
To express the potential difference in millivolts:
\[ V = 0.04 \, \text{V} = 40 \, \text{mV} \]

### Final Answer
The potential difference between points C and D is:
\[ V = 40 \, \text{mV} \]

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