Physics

Problem

The electric field

E

is measured at a point

P(0, 0, d)

generated due to various charge distributions and the dependence of

E

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. [Adv. 2018] ## LIST-I P.

E

is independent of

d

E \propto 1/d

E \propto 1/d^2

E \propto 1/d^3

## LIST-II 1. A point charge

Q

at the origin 2. A small dipole with point charges

Q

(0, 0, l)

and

-Q

(0, 0, -l)

. Take

2l \ll d

3. An infinite line charge coincident with the

x

-axis, with uniform linear charge density

\lambda

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

+\lambda

and the one along

(y=0, z=-l)

has a charge density

-\lambda

. Take

2l \ll d

5. Infinite plane charge coincident with the

xy

-plane with uniform surface charge density a.

P \to 5; Q \to 3, 4; R \to 1, S \to 2

P \to 5; Q \to 3; R \to 1, 4; S \to 2

P \to 5; Q \to 3; R \to 1, 2; S \to 4

P \to 4; Q \to 2, 3; R \to 1; S \to 5

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