Two metal spheres, one of radius R and the other of radius 2R, both have same surface charge density σ. They are brought in contact and separated. What will be the new surface charge densities on them?

<p><span data-teams="true">This is a long answer type question as classified in NCERT Exemplar</span></p><p>As we know that, &nbsp;<span contenteditable="false"> <math> <mi>σ</mi> </math> </span>=charge/Area</p><p>Q₁= <span contenteditable="false"> <math> <mi>σ</mi> </math> </span> (4<span contenteditable="false"> <math> <mi>π</mi> <mi>r</mi> </math> </span>²)</p><p>Q₂= <span contenteditable="false"> <math> <mi>σ</mi> </math> </span> (4<span contenteditable="false"> <math> <mi>π</mi> <mo> (</mo> <mn>2</mn> <mi>r</mi> <mo>)</mo> </math> </span>²)= 4Q₁</p><p>when they come in contact with each other potential being same and charge will be conserved.</p><p>So net charge is 5Q₁= 5 (<span contenteditable="false"> <math> <mi>σ</mi> </math> </span> (4<span contenteditable="false"> <math> <mi>π</mi> <mi>r</mi> </math> </span>²)</p><p>Also V₁=V₂</p><p>KQ₁/R=KQ₂/2R&nbsp; so Q₁=Q₂/2</p><p>Q₁= <span contenteditable="false"> <math> <mfrac> <mrow> <mrow> <mn>5</mn> </mrow> </mrow> <mrow> <mrow> <mn>3</mn> </mrow> </mrow> </mfrac> <mi> </mi> <mo> (</mo> <mi>σ</mi> </math> </span> (4<span contenteditable="false"> <math> <mi>π</mi> <mi>r</mi> </math> </span>²) and Q₂=<span contenteditable="false"> <math> <mfrac> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mn>3</mn> </mrow> </mrow> </mfrac> <mi> </mi> <mo> (</mo> <mi>σ</mi> </math> </span> (4<span contenteditable="false"> <math> <mi>π</mi> <mi>r</mi> </math> </span>²)</p><p><span contenteditable="false"> <math> <mi>σ</mi> </math> </span>=5<span contenteditable="false"> <math> <mi>σ</mi> </math> </span> <em>/3&nbsp; and <span contenteditable="false"> <math> <mi>σ</mi> </math> </span></em><em>&nbsp;=5<span contenteditable="false"> <math> <mi>σ</mi> </math> </span> </em><em>/6</em></p>

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