Electrostatics

Field line density decreases with increased distance from the wire while maintaining direct proportionality to their respective densities.

Field line density increases with increased distance from the wire, reversing proportionality to their respective densities due to limited extent of lines spreading outwards to infinity.

Field line density remains constant independent of distance from the wire and their respective densities since wires are infinitely long.

All wires produce an equal number of field lines per unit length regardless of variations in charged densities owing to uniformity of infinite extension.

Four times $V_0$

Remains as $V_0$

Twice $V_0$

Half of $V_0$

Ampere

Volt

Coulomb

Watt

$V = \frac{kq}{r^2} + C$

$V = \frac{kq}{r} + C$, where $C$ is a constant of integration determined by reference point

$V = \frac{kq^2}{r^3} + C$

$V = -\frac{kq}{r^2} + C$

It increases linearly with increasing $r$.

It decreases logarithmically with increasing $r$.

It decreases inversely with increasing $r$.

It remains constant regardless of $r$.

Conductor

Insulator

Semiconductor

Superconductor

Coulomb (C)

Volt (V)

Ampere (A)

Ohm (Ω)

$\Delta V = \left( \frac{\sigma}{4 \pi \varepsilon_{0}} \right) \ln \left( \frac{y_{2}}{y_{1}} \right)$

$\Delta V = - \left( \frac{\sigma}{2 \varepsilon_{0}} \right) (y_{2} - y_{1})$

$\Delta V = \left( \frac{\sigma}{4 \pi \varepsilon_{0}} \right) \left( \frac{1}{y_{1}} - \frac{1}{y_{2}} \right)$

$\Delta V = - \left( \frac{\sigma}{\varepsilon_{0}} \right) \frac{(y_{2}^{2} - y_{1}^{2})}{2}$

$\frac{\rho^2 R^4}{8 \pi \varepsilon_0}$

$\frac{3 \rho^2 R^5}{20 \varepsilon_0}$

$\frac{\rho^2 R^3}{6 \varepsilon_0}$

$\frac{\rho R^3}{4 \pi \varepsilon_0}$

They would have no effect on each other due to opposite signs

They would cancel each other creating no external fields

External effects would oscillate

They would double their combined external effects