find the work done by an external agent in slowly shifting a charge `q = 1 mu C` in the electric field ` vec E = 10^3 hat i Vm^-1` from the point `P(1,2) "to" Q(3, 4)`.

Explanation

To find the work done by an external agent in slowly shifting a charge \( q = 1 \, \mu C \) in the electric field \( \vec{E} = 10^3 \hat{i} \, V/m \) from the point \( P(1,2) \) to \( Q(3,4) \), we can follow these steps:

### Step 1: Understand the Work Done by an External Agent
The work done \( W \) by an external agent in moving a charge \( q \) in an electric field can be expressed as:
\[ W = q \cdot (V_f - V_i) \]
where \( V_f \) is the final electric potential and \( V_i \) is the initial electric potential.
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