Physics questions

Question

Derive an expression of the potential due to an electric dipole at a point lies on its axial position where r>a provided that the potential due to an infinity is 6 V

Answer 1

\(V_{net} = V_1 + V_2\)

\(= -\frac1{4\pi \epsilon_0} \frac q{r + a} + \frac 1{4\pi \epsilon_0} \frac q{r - a}\)

\(= \frac q{4\pi \epsilon_0}\left(\frac 1{r-a} - \frac 1{r + a}\right)\)

\(= \frac 1{4\pi \epsilon_0} q\left(\frac{r + a- r + a}{r^2 -a^2}\right)\)

\(= \frac 1{4\pi \epsilon_0} \frac{q.2a}{r^2 - a^2}\)

\(\because p = q.2 a\)

\(= \frac 1{4\pi \epsilon_0} \frac{p}{r^2 - a^2}\)

For r > a

\(v = \frac 1{4 \pi \epsilon_0} \frac p{r^2}\)