Two charges q and -3q are placed fixed on x-axis separated by distance d. where should a third charge 2q be placed such that it will not experience any force?

This is a Short Answer Type Questions as classified in NCERT Exemplar

Answer = $\frac{d}{2}$ (1+ $\sqrt[]{3}$ ) towards left.

Explanation -lets consider 2q charge is placed in between q and -3q, here it will definitely experience some force q charge repel 2q charge and -3q charge will attract 2q charge. So 2q charge will move towards -3q charge.

Now lets consider it to the left of q at some distance x, here the force experience by q is repulsive and force experience by -3q is attractive . so they cancel out each other and no net force is experience by 2q.

Thus, force of attraction by -3q = force of repulsion by q

$?$ k 2q q/x² = k 2q 3q/ (x+d)²

 

$?$ (x+d)² = 3x

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This is a Short Answer Type Questions as classified in NCERT Exemplar

Answer = $\frac{d}{2}$ (1+ $\sqrt[]{3}$ ) towards left.

Explanation -lets consider 2q charge is placed in between q and -3q, here it will definitely experience some force q charge repel 2q charge and -3q charge will attract 2q charge. So 2q charge will move towards -3q charge.

Now lets consider it to the left of q at some distance x, here the force experience by q is repulsive and force experience by -3q is attractive . so they cancel out each other and no net force is experience by 2q.

Thus, force of attraction by -3q = force of repulsion by q

$?$ k 2q q/x² = k 2q 3q/ (x+d)²

 

$?$ (x+d)² = 3x²

 

$?$ x² + d² + 2xd = 3x²

 

$?$ 2x² - 2dx – d² = 0

 

$?$ x = $\frac{d}{2}$ + $\frac{\sqrt[]{3}d}{2}$

 

$?$ x= $\frac{d}{2}$ (1+ $\sqrt[]{3}$ ) towards left.

 

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<p>This is a Short Answer Type Questions as classified in NCERT Exemplar</p><p><strong>Answer</strong> = <span contenteditable="false"> <math> <mfrac> <mrow> <mrow> <mi>d</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </mfrac> </math> </span> (1+<span contenteditable="false"> <math> <mroot> <mrow> <mrow> <mn>3</mn> </mrow> </mrow> <mrow></mrow> </mroot> </math> </span> ) towards left.</p><p><strong>Explanation</strong> -lets consider 2q charge is placed in between q and -3q, here it will definitely experience some force q charge repel 2q charge and -3q charge will attract 2q charge. So 2q charge will move towards -3q charge.</p><p>Now lets consider it to the left of q at some distance x, here the force experience by q is repulsive and force experience by -3q is attractive . so they cancel out each other and no net force is experience by 2q.</p><div><div><picture><source srcset="https://images.shiksha.com/mediadata/images/articles/1741779848php9g2Iya_480x360.jpeg" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/articles/1741779848php9g2Iya.jpeg" alt="" width="262" height="57"></picture></div><div><p>Thus, force of attraction by -3q = force of repulsion by q</p><p><span contenteditable="false"> <math> <mo>? </mo> <mi> </mi> </math> </span>k 2q q/x² = k 2q 3q/ (x+d)²</p><p>&nbsp;</p><p><span contenteditable="false"> <math> <mo>? </mo> </math> </span> (x+d)² = 3x²</p><p>&nbsp;</p><p><span contenteditable="false"> <math> <mo>? </mo> </math> </span>x² + d² + 2xd = 3x²</p><p>&nbsp;</p><p><span contenteditable="false"> <math> <mo>? </mo> </math> </span>2x² - 2dx – d² = 0</p><p>&nbsp;</p><p><span contenteditable="false"> <math> <mo>? </mo> </math> </span>x = <span contenteditable="false"> <math> <mfrac> <mrow> <mrow> <mi>d</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </mfrac> </math> </span>+<span contenteditable="false"> <math> <mfrac> <mrow> <mrow> <mroot> <mrow> <mrow> <mn>3</mn> </mrow> </mrow> <mrow></mrow> </mroot> <mi> </mi> <mi>d</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </mfrac> </math> </span></p><p>&nbsp;</p><p><span contenteditable="false"> <math> <mo>? </mo> </math> </span> x= <span contenteditable="false"> <math> <mfrac> <mrow> <mrow> <mi>d</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </mfrac> </math> </span> (1+ <span contenteditable="false"> <math> <mroot> <mrow> <mrow> <mn>3</mn> </mrow> </mrow> <mrow></mrow> </mroot> </math> </span>) towards left.</p><p>&nbsp;</p></div></div>

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