Ten charges are placed on the circumference of a circle of radius $R$ with constant angular separation between successive charges. Alternate charges $1,3,5,7,9$ have charge $(+q)$ each, while $2,4,6,8,10$ have charge $(-q)$ each. The potential $V$ and the electric field $E$ at the centre of the circle are respectively
(Take $V =0$ at infinity $)$
JEE MAIN 2020, Diffcult
Download our app for free and get started
Sol. Potential of centre $= V =\quad \Sigma\left(\frac{ kq }{ R }\right)$
$V _{ C }=\frac{ K (\Sigma q )}{ R }$
$V _{ C }=\frac{ K (0)}{ R }=0$
Electric field at centre $\overrightarrow{ E }_{ B }=\Sigma \overrightarrow{ E }$
Let $E$ be electric field produced by each charge at the centre, then resultant electric field will be
$E _{ C }=0,$ since equal electric field vectors are acting at equal angle so their resultant is equal to zero.
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
- 1An electric field $\vec E\, = (25 \hat i + 30 \hat j)\,NC^{-1}$ exists in a region of space. If the potential at the origin is taken to be zero then the potential at $x\, = 2\, m, y\, = 2\, m$ is......$volt$View Solution
- 2View SolutionWork done in moving a positive charge on an equipotential surface is
- 3The area of each plate of a parallel plate capacitor is $20\,cm^2$ and separation between the plates is $2\,mm$. If dielectric strength of air is $3 \times 10^6\,V/m,$ the maximum possible value of emf of the battery, which can be connected across the plates of this capacitor and the corresponding charge on the plates isView Solution
- 4If $OP = 1\,\,cm$ and $OS = 2\,\, cm$, work done by electric field in shifting a point charge $\frac {4\sqrt 2}{27}\,\, μC$ from point $P$ to $S$ in given figure isView Solution
- 5In the circuit shown, when the key $k $ is pressed at time $t = 0$, which of the following statements about current $I$ in the resistor $AB $ is trueView Solution
- 6A parallel plate capacitor with a dielectric slab completely occupying the space between the plates is charged by a battery and then disconnected. The slab is pulled out with a constant speed. Which of the following curves represent qualitatively the variation of the capacitance $C$ of the system with time?View Solution
- 7Two identical parallel plate capacitors, of capacitance $C$ each, have plates of area $A$, separated by a distance $d$. The space between the plates of the two capacitors, is filled with three dielectrics, of equal thickness and dielectric constants $K_1$ , $K_2$ and $K_3$ . The first capacitor is filled as shown in fig. $I$, and the second one is filled as shown in fig. $II$. If these two modified capacitors are charged by the same potential $V$, the ratio of the energy stored in the two, would be ( $E_1$ refers to capacitor $(I)$ and $E_2$ to capacitor $(II)$)View Solution
- 8A potential difference of $300\, volts$ is applied to a combination of $2.0\,\mu F$ and $8.0\,\mu F$ capacitors connected in series. The charge on the $2.0\,\mu F$ capacitor isView Solution
- 9A $6\,\mu F$ capacitor is charged from $10\;volts$ to $20\;volts$. Increase in energy will beView Solution
- 10The figure shows a diagonal symmetric arrangement of capacitors and a battery. If the potential of $C$ is zero, thenView Solution
