Q.Derive an expression for electrostatic potential due to an electric dipole. OR What is Fibre Optic Communication ? Write its merits and demerits.

(a) Superposing the potentials of a dipole's two point charges and simplifying for $r\gg a$ gives $V=\dfrac{1}{4\pi\varepsilon_0}\dfrac{p\cos\theta}{r^2}$; (b) fibre optic communication offers huge bandwidth and interference immunity but is fragile and requires precision installation. Both alternatives answered below.

(a) Electrostatic potential due to an electric dipole

1. Setup. A dipole has charges $-q$ at A and $+q$ at B, separated by $2a$, dipole moment $p=q(2a)$. Consider a general point P at distance $r$ from the dipole's centre O, where the line OP makes angle $\theta$ with the dipole axis (from $-q$ to $+q$).

2. Potential from each charge (using the cosine rule for distances, and the far-field/short-dipole approximation $r\gg a$):

$r_1 \approx r - a\cos\theta \ (\text{distance to } +q), \qquad r_2 \approx r + a\cos\theta \ (\text{distance to } -q)$

3. Net potential (superposition, potential is scalar):

$V = \dfrac{1}{4\pi\varepsilon_0}\left[\dfrac{q}{r_1} - \dfrac{q}{r_2}\right] = \dfrac{q}{4\pi\varepsilon_0}\left[\dfrac{1}{r-a\cos\theta}-\dfrac{1}{r+a\cos\theta}\right]$

4. Simplifying (combine over common denominator, then use $r\gg a$ so $r^2-a^2\cos^2\theta\approx r^2$):

$V = \dfrac{q}{4\pi\varepsilon_0}\cdot\dfrac{2a\cos\theta}{r^2-a^2\cos^2\theta} \approx \dfrac{1}{4\pi\varepsilon_0}\dfrac{(2aq)\cos\theta}{r^2} = \dfrac{1}{4\pi\varepsilon_0}\dfrac{p\cos\theta}{r^2}$

5. Special cases: on the axial line ($\theta=0$), $V=\dfrac{1}{4\pi\varepsilon_0}\dfrac{p}{r^2}$; on the equatorial line ($\theta=90°$), $V=0$.

(b) Fibre Optic Communication (FOC)

Principle. Information (voice, data, video), converted to a modulated light signal, is transmitted along a thin glass or plastic fibre. The fibre's core has a slightly higher refractive index than its surrounding cladding, so light entering within the acceptance angle undergoes repeated total internal reflection at the core-cladding boundary, guiding the light along the fibre's length over very long distances with minimal loss.

Merits

1. Enormous bandwidth/information-carrying capacity, since optical frequencies are far higher than radio/microwave frequencies.
2. Immune to electromagnetic interference -- unaffected by nearby power lines, radio signals, or lightning (since it carries light, not electric current). …