⚡️ What is Electrostatic Potential?
Picture any charge configuration creating an electric field. Now imagine gently (no acceleration!) sliding a unit positive test charge from far, far away (where the field is practically zero) to some point P. The work you do per unit charge is the electrostatic potential \(V\) at P. :contentReference[oaicite:0]{index=0}
Key points at a glance 😊
- The actual value of potential energy isn’t important—only the difference matters. You can shift the zero wherever convenient (we choose infinity). :contentReference[oaicite:1]{index=1}
- Potential difference between two points R and P is \( V_P – V_R = -\dfrac{U_P – U_R}{q} \). :contentReference[oaicite:2]{index=2}
- Because force is conservative, the work (and hence \(V\)) is **path-independent**. Move along any route you like! :contentReference[oaicite:3]{index=3}
- Bring a tiny test charge \(dq\), measure \(dW\), then \(V = \dfrac{dW}{dq}\). The result doesn’t depend on the test charge’s size. :contentReference[oaicite:4]{index=4}
🔍 Deriving \(V\) for a Point Charge
For a point charge \(Q\) at the origin, integrate the radial force from infinity to a distance \(r\). The friendly final formula is \[ V(r) = \frac{1}{4\pi\varepsilon_0}\,\frac{Q}{r}. \] Positive \(Q\) gives positive potential (you do work against repulsion); negative \(Q\) gives negative potential (the field helps you). :contentReference[oaicite:5]{index=5}
🎯 Why “Zero at Infinity” Helps
Choosing \(V=0\) at \(r\to\infty\) keeps numbers neat and comparisons easy. With that baseline, \[ W_{\infty\to P}= U_P – U_\infty = U_P \] and \[ V(P) = \frac{W_{\infty\to P}}{q}. \] :contentReference[oaicite:6]{index=6}
✨ High-Yield Ideas for NEET
- Reference Potential: Setting \(V=0\) at infinity simplifies most problems.
- Work–Potential Link: 1 volt = 1 joule per coulomb (from \(V = W/q\)).
- Point-Charge Formula: \(V(r)=\dfrac{1}{4\pi\varepsilon_0}\dfrac{Q}{r}\) — memorize it!
- Sign Sense: Positive \(Q\) → positive \(V\); negative \(Q\) → negative \(V\).
- Path Independence: Conservative nature of electrostatic force means only start and end points matter.
Keep practicing — you’ve got this! 💪⚡️
