Two identical thin rings each of radius R met | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The work done $W$ in moving a charge $q$ from the centre of the first ring $(O_1)$ to the centre of the second ring $(O_2)$ is given by $W = q(V_{

Vedclass · Accepted Answer

$\frac{q(Q_2 - Q_1)(\sqrt{2} - 1)}{\sqrt{2} \cdot 4\pi \varepsilon_0 R}$

Vedclass · Answer

(B) The work done $W$ in moving a charge $q$ from the centre of the first ring $(O_1)$ to the centre of the second ring $(O_2)$ is given by $W = q(V_{O_2} - V_{O_1})$.The potential at the centre of the first ring $(O_1)$ due to both rings is:$V_{O_1} = \frac{Q_1}{4\pi \varepsilon_0 R} + \frac{Q_2}{4\pi \varepsilon_0 \sqrt{R^2 + R^2}} = \frac{1}{4\pi \varepsilon_0 R} \left( Q_1 + \frac{Q_2}{\sqrt{2}} \right)$.The potential at the centre of the second ring $(O_2)$ due to both rings is:$V_{O_2} = \frac{Q_2}{4\pi \varepsilon_0 R} + \frac{Q_1}{4\pi \varepsilon_0 \sqrt{R^2 + R^2}} = \frac{1}{4\pi \varepsilon_0 R} \left( Q_2 + \frac{Q_1}{\sqrt{2}} \right)$.The potential difference is:$V_{O_2} - V_{O_1} = \frac{1}{4\pi \varepsilon_0 R} \left( Q_2 + \frac{Q_1}{\sqrt{2}} - Q_1 - \frac{Q_2}{\sqrt{2}} \right) = \frac{1}{4\pi \varepsilon_0 R} \left( (Q_2 - Q_1) - \frac{1}{\sqrt{2}}(Q_2 - Q_1) \right) = \frac{Q_2 - Q_1}{4\pi \varepsilon_0 R} \left( 1 - \frac{1}{\sqrt{2}} \right) = \frac{(Q_2 - Q_1)(\sqrt{2} - 1)}{\sqrt{2} \cdot 4\pi \varepsilon_0 R}$.Therefore,the work done is $W = \frac{q(Q_2 - Q_1)(\sqrt{2} - 1)}{\sqrt{2} \cdot 4\pi \varepsilon_0 R}$.

Two identical thin rings each of radius $R$ meters are coaxially placed at a distance $R$ meters apart. If $Q_1$ coulomb and $Q_2$ coulomb are respectively the charges uniformly spread on the two rings,the work done in moving a charge $q$ from the centre of one ring to that of other is

Similar Questions

If $4 \times 10^{20} \text{ eV}$ of energy is required to move a charge of $0.25 \text{ C}$ between two points,what will be the potential difference between them in volts?

If the potential of the inner shell of radius $r$ is $10\,V$ and that of the outer shell of radius $2r$ is $5\,V$, then the potential at the centre will be....$V$

Write an equation for the potential at a point in a uniformly charged spherical shell.

Define an electron Volt $(eV)$ and express its value in Joule $(J)$ units.

Four identical charges $+50\,\mu C$ each are placed,one at each corner of a square of side $2\,m$. How much external energy is required to bring another charge of $+50\,\mu C$ from infinity to the centre of the square? (Given $\frac{1}{4\pi\varepsilon_0} = 9 \times 10^9\,\frac{N\cdot m^2}{C^2}$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module