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4. Calculate the work done by the electric field

The work done by the electric field ($W_{AB}$) when a charge $Q$ moves from point A to point B is given by the formula $W_{AB} = Q(V_A - V_B)$, where $V_A$ is the potential at point A and $V_B$ is the potential at point B.

• Step 1: Identify the given values and convert units. The charge is $Q = 12 \, \mu\text{C} = 12 \times 10^{-6} \, \text{C}$. The potential at point A is $V_A = 10 \, \text{V}$. The potential at point B is $V_B = 6 \, \text{V}$.

• Step 2: Apply the formula for work done by the electric field. The formula is:

  $$W_{AB} = Q(V_A - V_B)$$

• Step 3: Substitute the values and calculate the work done.

  $$W_{AB} = (12 \times 10^{-6} \, \text{C}) (10 \, \text{V} - 6 \, \text{V})$$ $$W_{AB} = (12 \times 10^{-6} \, \text{C}) (4 \, \text{V})$$ $$W_{AB} = 48 \times 10^{-6} \, \text{J}$$

• Step 4: Express the result in appropriate units.

  $$W_{AB} = 48 \, \mu\text{J}$$

  The work done by the electric field is $\text{48 } \mu\text{J}$.