 # Potential due to a Point Charge, Electric Dipole and system of charges

• The potential at a point due to an Electric dipole is \tt V=\frac{P\cos\theta}{4\pi \varepsilon_{0}r^{2}}
• For a point on the axial line is \tt V=\frac{P}{4\pi \varepsilon_{0}r^{2}}
• For a point on the equatorial line is V = O
• The surface over which the potential is same as called equipotential surface
• Electrostatic potential due to infinite long changed wire at “r” \tt V=\frac{\lambda}{2\pi e_{0}}\log_{e}^{r}+\ k {k = constant}
• The Electrostatic Potential due to a thin infinite non conducting plane sheet \tt V=-\frac{\sigma}{2\varepsilon_{0}}r
• The Potential at a point outside the sphere is \tt V=\frac{1}{4\pi \varepsilon_{0}}.\frac{Q}{r}=\frac{\sigma\ R^{2}}{\varepsilon_{0}r} (R = Radians)
• The Potential at a point on the surface of sphere \tt V=\frac{1}{4\pi e_{0}}.\frac{Q}{R}=\frac{\sigma\ R}{\varepsilon_{0}}
• The Potential inside the sphere \tt V=\frac{1}{4\pi \varepsilon_{0}}.\frac{Q\left(3R^{2}-r^{2}\right)}{2R^{3}}
• V centre > V surface > V out (sphere)
• (Sphere)

• Electric Potential’s unit is volt.
• When 1 Joule of work is done in bringing 1 unit coulomb of charge then the potential is said to be 1 volt.

### View the Topic in this video From 01:39 To 36:51

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1. Potential due to System of charges
Let there be a number of point charges q1, q2, q3, ........ qn at distances r1, r2, r3 ......, rn respectively from the point P, where electric potential is given by
V = \frac{1}{4\pi \varepsilon_{0}}\sum_{i = 1}^{n} \frac{q_{i}}{r_{i}}

2. Potential Gradient
The rate of change of potential with distance in electric field is called potential gradient.
Potential gradient = \frac{dV}{dr}

3. Relation between potential gradient and electric field intensity is given by
E = -\left[\frac{dV}{dr}\right]

4. The net torque experienced by the dipole is
τ = pE sin θ
\overrightarrow{\tau} = \overrightarrow{p} \times \overrightarrow{E}

5. Potential Difference:
V_{ab} = -\int_{a}^{b} \overrightarrow{E}.d \ \overrightarrow{r}

6. Work done in Rotationg an Electric Dipole in a unifrom electric field
⇒ Wexternal = PE(1 − cos θ)