The $E - r$ curve for an infinite linear charge distribution will be

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Solution

The correct option is C
For infinite charge distribution , field at any point other than its axis is,

$E = \frac{λ}{2 π ε_{0} r}$

$∴ E \propto \frac{1}{r}$

Hence $E - r$ curve is a rectangular hyperbola.

 Hence, (c) is the correct answer.

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_{1}

_{2}

_{3}

λ

σ

_{1} (r_{0}) = E_{2} (r_{0}) = E_{3} (r_{0})

_{0}

(E)

(r)

List - I	List - II
(P) E is independent of d	(1) A point charge Q at the origin
(Q) $E \propto \frac{1}{d}$	(2) A small dipole with point charges Q at $(0, 0, l)$ and - Q at $(0, 0, - l)$ . Take $2 l << d$
(R) $E \propto \frac{1}{d^{2}}$	(3) A infinite line charge coincident with the x-axis, with uniform linear charge density $λ$ .
(S) $E \propto \frac{1}{d^{3}}$	(4) Two infinite wires carrying uniform linear charge density parallel to the x-axis. The one along ( $y = 0, z = l$ ) has a charge density + $λ$ and the one along $(y = 0, z = - l)$ has a charge density $- λ$ . Take $2 l << d$
	(5) Infinite plane charge coincident with the xy-plane with uniform surface charge density