A non-conducting ring of radius $0.5\,m$ carries a total charge of $1.11 \times {10^{ - 10}}\,C$ distributed non-uniformly on its circumference producing an electric field $\vec E$ everywhere in space. The value of the line integral $\int_{l = \infty }^{l = 0} {\, - \overrightarrow E .\overrightarrow {dl} } \,(l = 0$ being centre of the ring) in volt is
A$2$
B$-1$
C$-2$
D$0$
IIT 1997, Medium
Download our app for free and get started
A$2$
a (a) $\int_{\, - \infty }^{\,0} { - \overrightarrow E \, \cdot \overrightarrow {dl} } $ $=$ potential at centre of non-conducting ring
$ = \frac{1}{{4\pi {\varepsilon _0}}} \times \frac{q}{r} = \frac{{9 \times {{10}^9} \times 1.11 \times {{10}^{ - 10}}}}{{0.5}} = 2\,volt$
Download our app
and 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.*
A point chargr $Q$ is fixed A small charge $q$ and mass $m$ is given a velocity $v_0$ from infinity & perpendicular distance $r_0$ as shown. If distance of closest approach is $r_0/2$. The value of $q$ is [Given $mv_0^2 = \frac{{{Q^2}}}{{4\pi { \in _0}\,{r_0}}}$]
The energy and capacity of a charged parallel plate capacitor are $U$ and $C$ respectively. Now a dielectric slab of $\in _r = 6$ is inserted in it then energy and capacity becomes (Assume charge on plates remains constant)
Two positrons $(e^+)$ and two protons $(p)$ are kept on four corners of a square of side $a$ as shown in figure. The mass of proton is much larger than the mass of positron. Let $q$ denotes the charge on the proton as well as the positron then the kinetic energies of one of the positrons and one of the protons respectively after a very long time will be-
A capacitor of capacitance $C_1 = 1\ \mu F$ can with stand maximum voltage $V_1= 6\ kV$ (kilo-volt) and another capacitor of capacitance $ C_2 = 3\ \mu F$ can withstand maximum voltage $V_2 = 4\ kV$. When the two capacitors are connected in series, the combined system can withstand a maximum voltage of......$kV$
This question contains Statement$-1$ and Statement$-2$. Of the four choices given after the statements, choose the one that best describes the two statements.
Statement$-1$ : For a charged particle moving from point $P$ to point $Q$, the net work done by an electrostatic field on the particle is independent of the path connecting point $P$ to point $Q$.
Statement$-2$ : The net work done by a conservative force on an object moving along a closed loop is zero.