Find the work done by some external force in moving a charge `q=2muC` from infinity to a point where electric potential is `10^4` V.

Explanation

To find the work done by an external force in moving a charge \( q = 2 \, \mu C \) from infinity to a point where the electric potential is \( 10^4 \, V \), we can follow these steps:

### Step 1: Understand the relationship between work done and electric potential
The work done \( W \) by an external force in moving a charge \( q \) in an electric field is given by the change in potential energy, which can be expressed as:
\[ W = q \cdot \Delta V \]
where \( \Delta V \) is the change in electric potential.

### Step 2: Identify the initial and final potentials
When the charge is at infinity, the electric potential \( V_i \) is \( 0 \, V \). The final potential \( V_f \) at the point we are moving the charge to is given as \( 10^4 \, V \).

### Step 3: Calculate the change in potential
The change in potential \( \Delta V \) can be calculated as:
\[ \Delta V = V_f - V_i = 10^4 \, V - 0 \, V = 10^4 \, V \]

### Step 4: Substitute the values into the work done formula
Now, substituting the values into the work done formula:
- Charge \( q = 2 \, \mu C = 2 \times 10^{-6} \, C \)
- Change in potential \( \Delta V = 10^4 \, V \)

Thus, the work done \( W \) is:
\[ W = q \cdot \Delta V = (2 \times 10^{-6} \, C) \cdot (10^4 \, V) \]

### Step 5: Perform the calculation
Calculating the above expression:
\[ W = 2 \times 10^{-6} \times 10^4 = 2 \times 10^{-2} \, J \]

### Conclusion
The work done by the external force in moving the charge from infinity to the point where the electric potential is \( 10^4 \, V \) is:
\[ W = 0.02 \, J \quad \text{or} \quad 2 \times 10^{-2} \, J \]

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