Electrostatics Ques 5
- 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 | |
|---|---|---|
| P.$E$ 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 $(0,0,-1)$. (Take, $2 l«d)$ |
|
| R. $E \propto \frac{1}{d^2}$ | 3.An infinite line charge coincident with the $X$-axis, with uniform linear charge density $\lambda$. |
|
| S. $E \propto \frac{1}{d^3}$ | Two infinite wires carrying a 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, $2 l«d$). |
(2018 Adv.)
(a) $\mathrm{P} \rightarrow 5 ; \mathrm{Q} \rightarrow 3,4 ; \mathrm{R} \rightarrow 1 ; \mathrm{S} \rightarrow 2$
(b) $\mathrm{P} \rightarrow 5 ; \mathrm{Q} \rightarrow 3 ; \quad \mathrm{R} \rightarrow 1,4 ; \mathrm{S} \rightarrow 2$
(c) $\mathrm{P} \rightarrow 5 ; \mathrm{Q} \rightarrow 3 ; \quad \mathrm{R} \rightarrow 1,2 ; \mathrm{S} \rightarrow 4$
(d) $\mathrm{P} \rightarrow 4 ; \mathrm{Q} \rightarrow 2,3 ; \mathrm{R} \rightarrow 1 ; \mathrm{S} \rightarrow 5$
Show Answer
Answer:
Correct Answer: 5.( b )
Solution:
- List-II
(1) $E=\frac{1}{4 \pi \varepsilon_0} \frac{Q}{d^2}$
$\Rightarrow E \propto \frac{1}{d^2}$
(2) $E_{\text {axis }}=\frac{1}{4 \pi \varepsilon_0} \frac{2 Q(2 l)}{d^3}$
$\Rightarrow \quad E \propto \frac{1}{d^3}$
(3) $E=\frac{\lambda}{2 \pi \varepsilon_0 d} \Rightarrow E \propto \frac{1}{d}$
(4) $E=\frac{\lambda}{2 \pi \varepsilon_0(d-l)}-\frac{\lambda}{2 \pi \varepsilon_0(d+l)}=\frac{\lambda(2 l)}{2 \pi \varepsilon_0 d^2}$
$\Rightarrow E \propto \frac{1}{d^2}$
(5) $E=\frac{\sigma}{2 \varepsilon_0} \Rightarrow$ E is independent of $d$
BETA
