The electric field E is measured at a point P ( 0,0 , d ) , generated due to various charge distributions and the dependence of E on d is found to be different for different charge distributions. List-I contains different relations between E and d. List-II describes different electric charge…

Question

The electric field E is measured at a point P ( 0,0 , d ) , generated due to various charge distributions and the dependence of E on d is found to be different for different charge distributions. List-I contains different relations between E and d. List-II describes different electric charge distributions, along with their locations. Match the functions in List-I with the related charge distributions in List-II. LIST -I LIST -II A) E is independent of d P) A point charge at the origin B) E &#8733; 1 d Q) A small dipole with point charges Q at 0,0 , l &#160; a n d - Q a t 0 , &#160; 0 , l . T a k e &#160; 2 l &#8810; d C) E &#8733; 1 d 2 R) An infinite line charge coincident with the x &ndash; axis, with uniform linear charge density &#955; D) E &#8733; 1 d 3 S) Two infinite wires carrying uniform linear charge density parallel to the x &ndash; axis. The one along y = 0 , z = l has a charge density + &#955; and the one along y = 0 , z = - l has a charge density &#8211; &#955; . Take 2 l &#8810; d T) Infinite plane charge coincident with the xy &ndash; plane with uniform surface charge density

Aicharya · Accepted Answer

(i) Point charge E = K Q d 2 ⇒ E ∝ 1 d 2 ( i i ) Dipole E = 2 k p d 3 1 + 3 cos 2 ⁡ θ E ∝ 1 d 3 for dipole ( i i i ) For line charge E = 2 k λ d E ∝ 1 d (iv) Two line charge E = 2 k λ d - l - 2 K λ d + l = 2 K l d + l - d + l d 2 - l 2 E = 2 K λ 2 l d 2 1 - l 2 d 2 E ∝ 1 d 2 (v) Electric field due to sheet ∈ = σ 2 ∈ 0 ∈ = v is independent of r `

The electric field E is measured at a point P ( 0,0 , d ) , generated due to various charge distributions…

Solution

	LIST -I		LIST -II
A)	E is independent of d	P)	A point charge at the origin
B)	$E \propto \frac{1}{d}$	Q)	A small dipole with point charges $Q$ at $(0,0, l) a n d - Q a t (0, 0, l) . T a k e 2 l ≪ d$
C)	$E \propto \frac{1}{d^{2}}$	R)	An infinite line charge coincident with the x – axis, with uniform linear charge density $λ$
D)	$E \propto \frac{1}{d^{3}}$	S)	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 $2 l ≪ d$
		T)	Infinite plane charge coincident with the xy – plane with uniform surface charge density