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Electrostatics Physics Electrostatic Potential and Capacitance Physics Class 12th

Two identical positive charge Q each are fixed at a distance of ‘2a’ apart from each other. Another point charge q₀ with mass ‘m’ is placed at midpoint between two fixed charges. For a small displacement along the line joining the fixed charges, the charge q₀ executes SHM. The time period of oscillation of charge q₀ will be:

Option 1 -

$\sqrt[]{\frac{4 π^{3} ε_{0} m a^{3}}{q_{0} Q}}$

Option 2 -

$\sqrt[]{\frac{q_{0} Q}{4 π^{3} ε_{0} m a^{3}}}$

Option 3 -

$\sqrt[]{\frac{2 π^{2} ε_{0} m a^{3}}{q_{0} Q}}$

Option 4 -

$\sqrt[]{\frac{8 π^{3} ε_{0} m a^{3}}{q_{0} Q}}$

8 Views | Posted 2 months ago

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4 Answers
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Answered by

alok kumar singh | Contributor-Level 10

2 months ago

Correct Option - 1

Detailed Solution:

$F_{R} = {\frac{k Q q_{0}}{{(a - x)}^{2}} - \frac{k Q q_{0}}{{(a + x)}^{2}}}$

$= - k Q q_{0} {\frac{a^{2} + x^{2} + 2 a x - a^{2} - x^{2} + 2 a x}{(a^{2} - x^{2})}}$

$F_{R} = - \frac{k Q q_{0} (4 a x)}{{(a^{2} - x^{2})}^{2}}$

$T = 2 π \sqrt[]{\frac{a^{3} m}{4 k Q q_{0}} = \sqrt[]{\frac{4 π^{2} a^{3} m \times 4 π ε_{0}}{4 Q q_{0}}}} = \sqrt[]{\frac{4 π^{3} ε_{0} m a^{3}}{Q q_{0}}}$

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Answered by

alok kumar singh | Contributor-Level 10

2 months ago

Correct Option - 1

Detailed Solution:

$F_{R} = {\frac{k Q q_{0}}{{(a ? x)}^{2}} ? \frac{k Q q_{0}}{{(a + x)}^{2}}}$

$= ? k Q q_{0} {\frac{a^{2} + x^{2} + 2 a x ? a^{2} ? x^{2} + 2 a x}{(a^{2} ? x^{2})}}$

$F_{R} = ? \frac{k Q q_{0} (4 a x)}{{(a^{2} ? x^{2})}^{2}}$

$T = 2 ? \sqrt[]{\frac{a^{3} m}{4 k Q q_{0}} = \sqrt[]{\frac{4 ?^{2} a^{3} m * 4 ? ?_{0}}{4 Q q_{0}}}} = \sqrt[]{\frac{4 ?^{3} ?_{0} m a^{3}}{Q q_{0}}}$

0 Upvotes 0 Downvotes

Answered by

alok kumar singh | Contributor-Level 10

2 months ago

Correct Option - 1

Detailed Solution:

$F_{R} = {\frac{k Q q_{0}}{{(a ? x)}^{2}} ? \frac{k Q q_{0}}{{(a + x)}^{2}}}$

$= ? k Q q_{0} {\frac{a^{2} + x^{2} + 2 a x ? a^{2} ? x^{2} + 2 a x}{(a^{2} ? x^{2})}}$

$F_{R} = ? \frac{k Q q_{0} (4 a x)}{{(a^{2} ? x^{2})}^{2}}$

$T = 2 ? \sqrt[]{\frac{a^{3} m}{4 k Q q_{0}} = \sqrt[]{\frac{4 ?^{2} a^{3} m * 4 ? ?_{0}}{4 Q q_{0}}}} = \sqrt[]{\frac{4 ?^{3} ?_{0} m a^{3}}{Q q_{0}}}$

0 Upvotes 0 Downvotes

Answered by

alok kumar singh | Contributor-Level 10

2 months ago

Correct Option - 1

Detailed Solution:

$F_{R} = {\frac{k Q q_{0}}{{(a ? x)}^{2}} ? \frac{k Q q_{0}}{{(a + x)}^{2}}}$

$= ? k Q q_{0} {\frac{a^{2} + x^{2} + 2 a x ? a^{2} ? x^{2} + 2 a x}{(a^{2} ? x^{2})}}$

$F_{R} = ? \frac{k Q q_{0} (4 a x)}{{(a^{2} ? x^{2})}^{2}}$

$T = 2 ? \sqrt[]{\frac{a^{3} m}{4 k Q q_{0}} = \sqrt[]{\frac{4 ?^{2} a^{3} m * 4 ? ?_{0}}{4 Q q_{0}}}} = \sqrt[]{\frac{4 ?^{3} ?_{0} m a^{3}}{Q q_{0}}}$

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