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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)`.

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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 Electric Field The electric field \( \vec{E} = 10^3 \hat{i} \, V/m \) indicates that the field is uniform and directed along the positive x-axis. This means that the force acting on the charge will also be in the same direction. ### Step 2: Calculate the Displacement The displacement \( \vec{d} \) from point \( P(1,2) \) to point \( Q(3,4) \) can be calculated as: \[ ...
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