Electric Potential and Work Done Simulation
This interactive simulation demonstrates the concepts from Example 2.1, showing how to calculate electric potential and the work done in moving a charge.
Simulation
Select Path for Bringing Charge:
Potential Calculation:
\[ V = \frac{1}{4\pi\epsilon_0} \frac{Q}{r} \]
\[ V = 9 \times 10^9 \times \frac{4 \times 10^{-7}}{0.09} \]
\[ V = 4 \times 10^4 \, \text{V} \]
Work Done Calculation:
\[ W = qV \]
\[ W = 2 \times 10^{-9} \times 4 \times 10^4 \]
\[ W = 8 \times 10^{-5} \, \text{J} \]
Note: The work done is path independent.
Solution to Example 2.1
(a) Calculate the potential at point P:
\[ V = \frac{1}{4\pi\epsilon_0} \frac{Q}{r} = 9 \times 10^9 \, \text{Nm}^2 \, \text{C}^{-2} \times \frac{4 \times 10^{-7} \, \text{C}}{0.09 \, \text{m}} \]
\[ = 4 \times 10^4 \, \text{V} \]
(b) Work done in bringing a charge from infinity to point P:
\[ W = qV = 2 \times 10^{-9} \, \text{C} \times 4 \times 10^4 \, \text{V} \]
\[ = 8 \times 10^{-5} \, \text{J} \]
No, work done will be path independent. Any arbitrary infinitesimal path can be resolved into two perpendicular displacements: One along \(\mathbf{r}\) and another perpendicular to \(\mathbf{r}\). The work done corresponding to the later will be zero.