SATHEE: Electrostatics 7 Question 15

Electrostatics 7 Question 15

15. Two identical thin rings, each of radius $R$ , are coaxially placed a distance $R$ apart. If $Q_{1}$ and $Q_{2}$ 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 the other is

(1992, 2M)

(a) zero

(b) $\frac{q (Q_{1} - Q_{2}) (\sqrt{2} - 1)}{\sqrt{2} (4 π ε_{0} R)}$

(d) $q (Q_{1} / Q_{2}) (\sqrt{2} + 1) \sqrt{2} (4 π ε_{0} R)$

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Answer:

Correct Answer: 15. (b)

Solution:

$V_{C_{1}} = V_{Q_{1}} + V_{Q_{2}} = \frac{1}{4 π ε_{0}} \frac{Q_{1}}{R} + \frac{1}{4 π ε_{0}} \frac{Q_{2}}{R \sqrt{2}}$

$= \frac{1}{4 π ε_{0} R} Q_{1} + \frac{Q_{2}}{\sqrt{2}}$

Similarly $V_{C_{2}} = \frac{1}{4 π ε_{0} R} Q_{2} + \frac{Q_{1}}{\sqrt{2}}$

$∴ Δ V = V_{C_{1}} - V_{C_{2}} = \frac{1}{4 π ε_{0} R} (Q_{1} - Q_{2}) - \frac{1}{\sqrt{2}} (Q_{1} - Q_{2})$

$\begin{aligned} = \frac{Q_{1} - Q_{2}}{\sqrt{2} (4 π ε_{0} R)} (\sqrt{2} - 1) \\ W & = q Δ V = q (Q_{1} - Q_{2}) (\sqrt{2} - 1) / \sqrt{2} (4 π ε_{0} R) \end{aligned}$

Electrostatics 7 Question 15

15. Two identical thin rings, each of radius $R$ , are coaxially placed a distance $R$ apart. If $Q_{1}$ and $Q_{2}$ 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 the other is

Answer:

Solution:

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Electrostatics 7 Question 15

15. Two identical thin rings, each of radius R, are coaxially placed a distance R apart. If Q1 and Q2 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 the other is

Answer:

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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15. Two identical thin rings, each of radius $R$ , are coaxially placed a distance $R$ apart. If $Q_{1}$ and $Q_{2}$ 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 the other is