For an infinite line of charge having charge density $\lambda $ lying along $x-$ axis, the work required in moving charge $q$ from $C$ to $A$ along arc $CA$ is :-
Diffcult
Download our app for free and get started
$\mathrm{B} $ and $ \mathrm{C}$ are equipotential and field is conservative, therefore:
$\therefore \mathrm{W}_{\mathrm{CA}}=\mathrm{W}_{\mathrm{BA}^{-}}=-\int_{2 \mathrm{a}}^{\mathrm{a}} \frac{\lambda}{2 \pi \varepsilon_{0} \mathrm{r}} \mathrm{q} \mathrm{dr}=\frac{\mathrm{q} \lambda}{2 \pi \varepsilon_{0}} \operatorname{In} 2$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1A parallel plate capacitor with plate area $'A'$ and distance of separation $'d'$ is filled with a dielectric. What is the capacity of the capacitor when permittivity of the dielectric varies as :View Solution
$\varepsilon(x)=\varepsilon_{0}+k x, \text { for }\left(0\,<\,x \leq \frac{d}{2}\right)$
$\varepsilon(x)=\varepsilon_{0}+k(d-x)$, for $\left(\frac{d}{2} \leq x \leq d\right)$
- 2A $10\, \mu F$ capacitor is fully charged to a potential difference of $50\, V$. After removing the source voltage it is connected to an uncharged capacitor in parallel. Now the potential difference across them becomes $20\, V$. The capacitance of the second capacitor is......$\mu F$View Solution
- 3Two identical capacitors are joined in parallel, charged to potential $V$, separated and then, connected in series, $i.e.$, the positive plate of one is connected to the negative plate of the other. ThenView Solution
- 4The capacity of an air condenser is $2.0\, \,\mu F$. If a medium is placed between its plates. The capacity becomes $ 12\, \,\mu F$. The dielectric constant of the medium will beView Solution
- 5View SolutionValue of potential at a point due to a point charge is
- 6The electric potential $V(x)$ in a region around the origin is given by $V(x) = 4x^2\,volts$ . The electric charge enclosed in a cube of $1\,m$ side with its centre at the origin is (in coulomb)View Solution
- 7Three capacitors each of capacitance $C$ and of breakdown voltage $V$ are joined in series. The capacitance and breakdown voltage of the combination will beView Solution
- 8For two infinitely long charged parallel sheets, the electric field at $P$ will beView Solution
- 9The distance between the two plates of a parallel plate capacitor is doubled and the area of each plate is halved. If $C$ is its initial capacitance, its final capacitance is equal toView Solution
- 10In a uniform electric field, a cube of side $1\ cm$ is placed. The total energy stored in the cube is $8.85\ μJ$ . The electric field is parallel to four of the faces of the cube. The electric flux through any one of the remaining two faces isView Solution