Electrostatics of Conductors
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PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359439 Three concentric conducting spherical shells have radii \(r\),\(2r\) and \(3r\) and charges \({q_1},{q_2}\) and \({q_3}\) respectively. The innermost and outermost shells are earthed as shown in the figure. The charges given are after earthing. Select the correct alternative.
supporting img

1 \({q_1} + {q_3} = - {q_2}\)
2 \({q_1} = - {q_2}\)
3 \(\frac{{{q_3}}}{{{q_2}}} = \frac{{ - 1}}{3}\)
4 None of these
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359440 A spherical capacitor is made of two conducting spherical shells of radii \(a\) and \(b\).The space between the shells is filled with a dielectric of dielectric constant \(K\) upto a radius \(b\) as shown in figure. Calculate the capacitance.
supporting img

1 \(\frac{{K4\pi {\varepsilon _0}abc}}{{Ka\left( {c - b} \right) + c\left( {b - a} \right)}}\)
2 \(\frac{{K4\pi {\varepsilon _0}abc}}{{Kab + bc}}\)
3 \(\frac{{K4\pi {\varepsilon _0}abc}}{{{a^2} + {b^2} + {c^2}}}\)
4 None of these
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359441 A small conducting sphere lying concentrically inside a bigger hollow conducting sphere of radius \(R\). The bigger and smaller spheres are charged with \(Q\) and \(q(Q > q)\) and are insulated from each other, The potential difference between the spheres will be

1 \(\frac{1}{{4\pi {\varepsilon _0}}}\left( {\frac{q}{r}\; - \;\frac{Q}{R}} \right)\)
2 \(\frac{1}{{4\pi {\varepsilon _0}}}\left( {\frac{Q}{R}\; + \;\frac{q}{r}} \right)\)
3 \(\frac{1}{{4\pi {\varepsilon _0}}}\left( {\frac{q}{r}\; - \;\frac{q}{R}} \right)\)
4 \(\frac{1}{{4\pi {\varepsilon _0}}}\left( {\frac{q}{R}\; - \;\frac{Q}{r}} \right)\)
KCET - 2008
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359442 Figure shows three spherical and equipotential surfaces \(A, B\) and \(C\) round a point charge \(q\). The potential difference \(V_{A}-V_{B}=V_{B}-V_{C}\). If \(t_{1}\) and \(t_{2}\) be the distances between them, then
supporting img

1 \(t_{1}=t_{1}\)
2 \(t_{1}>t_{2}\)
3 \(t_{1} < t_{2}\)
4 \(t_{1} \leq t_{2}\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359443 Three concentric metal shells \(A, B\) and \(C\) of respective radii \(a,b\) and \(c\) have surface charge densities \( + \sigma , - \sigma \) and \( + \sigma \) respectively. The potential of shell \(B\) is :

1 \(\frac{\sigma }{{{\varepsilon _0}}}\left[ {\frac{{{a^2} - {b^2}}}{b} + c} \right]\)
2 \(\frac{\sigma }{{{\varepsilon _0}}}\left[ {\frac{{{b^2} - {c^2}}}{b} + a} \right]\)
3 \(\frac{\sigma }{{{\varepsilon _0}}}\left[ {\frac{{{b^2} - {c^2}}}{c} + a} \right]\)
4 \(\frac{\sigma }{{{\varepsilon _0}}}\left[ {\frac{{{a^2} - {b^2}}}{a} + c} \right]\)
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PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359439 Three concentric conducting spherical shells have radii \(r\),\(2r\) and \(3r\) and charges \({q_1},{q_2}\) and \({q_3}\) respectively. The innermost and outermost shells are earthed as shown in the figure. The charges given are after earthing. Select the correct alternative.
supporting img

1 \({q_1} + {q_3} = - {q_2}\)
2 \({q_1} = - {q_2}\)
3 \(\frac{{{q_3}}}{{{q_2}}} = \frac{{ - 1}}{3}\)
4 None of these
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359440 A spherical capacitor is made of two conducting spherical shells of radii \(a\) and \(b\).The space between the shells is filled with a dielectric of dielectric constant \(K\) upto a radius \(b\) as shown in figure. Calculate the capacitance.
supporting img

1 \(\frac{{K4\pi {\varepsilon _0}abc}}{{Ka\left( {c - b} \right) + c\left( {b - a} \right)}}\)
2 \(\frac{{K4\pi {\varepsilon _0}abc}}{{Kab + bc}}\)
3 \(\frac{{K4\pi {\varepsilon _0}abc}}{{{a^2} + {b^2} + {c^2}}}\)
4 None of these
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359441 A small conducting sphere lying concentrically inside a bigger hollow conducting sphere of radius \(R\). The bigger and smaller spheres are charged with \(Q\) and \(q(Q > q)\) and are insulated from each other, The potential difference between the spheres will be

1 \(\frac{1}{{4\pi {\varepsilon _0}}}\left( {\frac{q}{r}\; - \;\frac{Q}{R}} \right)\)
2 \(\frac{1}{{4\pi {\varepsilon _0}}}\left( {\frac{Q}{R}\; + \;\frac{q}{r}} \right)\)
3 \(\frac{1}{{4\pi {\varepsilon _0}}}\left( {\frac{q}{r}\; - \;\frac{q}{R}} \right)\)
4 \(\frac{1}{{4\pi {\varepsilon _0}}}\left( {\frac{q}{R}\; - \;\frac{Q}{r}} \right)\)
KCET - 2008
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359442 Figure shows three spherical and equipotential surfaces \(A, B\) and \(C\) round a point charge \(q\). The potential difference \(V_{A}-V_{B}=V_{B}-V_{C}\). If \(t_{1}\) and \(t_{2}\) be the distances between them, then
supporting img

1 \(t_{1}=t_{1}\)
2 \(t_{1}>t_{2}\)
3 \(t_{1} < t_{2}\)
4 \(t_{1} \leq t_{2}\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359443 Three concentric metal shells \(A, B\) and \(C\) of respective radii \(a,b\) and \(c\) have surface charge densities \( + \sigma , - \sigma \) and \( + \sigma \) respectively. The potential of shell \(B\) is :

1 \(\frac{\sigma }{{{\varepsilon _0}}}\left[ {\frac{{{a^2} - {b^2}}}{b} + c} \right]\)
2 \(\frac{\sigma }{{{\varepsilon _0}}}\left[ {\frac{{{b^2} - {c^2}}}{b} + a} \right]\)
3 \(\frac{\sigma }{{{\varepsilon _0}}}\left[ {\frac{{{b^2} - {c^2}}}{c} + a} \right]\)
4 \(\frac{\sigma }{{{\varepsilon _0}}}\left[ {\frac{{{a^2} - {b^2}}}{a} + c} \right]\)
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PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359439 Three concentric conducting spherical shells have radii \(r\),\(2r\) and \(3r\) and charges \({q_1},{q_2}\) and \({q_3}\) respectively. The innermost and outermost shells are earthed as shown in the figure. The charges given are after earthing. Select the correct alternative.
supporting img

1 \({q_1} + {q_3} = - {q_2}\)
2 \({q_1} = - {q_2}\)
3 \(\frac{{{q_3}}}{{{q_2}}} = \frac{{ - 1}}{3}\)
4 None of these
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359440 A spherical capacitor is made of two conducting spherical shells of radii \(a\) and \(b\).The space between the shells is filled with a dielectric of dielectric constant \(K\) upto a radius \(b\) as shown in figure. Calculate the capacitance.
supporting img

1 \(\frac{{K4\pi {\varepsilon _0}abc}}{{Ka\left( {c - b} \right) + c\left( {b - a} \right)}}\)
2 \(\frac{{K4\pi {\varepsilon _0}abc}}{{Kab + bc}}\)
3 \(\frac{{K4\pi {\varepsilon _0}abc}}{{{a^2} + {b^2} + {c^2}}}\)
4 None of these
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359441 A small conducting sphere lying concentrically inside a bigger hollow conducting sphere of radius \(R\). The bigger and smaller spheres are charged with \(Q\) and \(q(Q > q)\) and are insulated from each other, The potential difference between the spheres will be

1 \(\frac{1}{{4\pi {\varepsilon _0}}}\left( {\frac{q}{r}\; - \;\frac{Q}{R}} \right)\)
2 \(\frac{1}{{4\pi {\varepsilon _0}}}\left( {\frac{Q}{R}\; + \;\frac{q}{r}} \right)\)
3 \(\frac{1}{{4\pi {\varepsilon _0}}}\left( {\frac{q}{r}\; - \;\frac{q}{R}} \right)\)
4 \(\frac{1}{{4\pi {\varepsilon _0}}}\left( {\frac{q}{R}\; - \;\frac{Q}{r}} \right)\)
KCET - 2008
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359442 Figure shows three spherical and equipotential surfaces \(A, B\) and \(C\) round a point charge \(q\). The potential difference \(V_{A}-V_{B}=V_{B}-V_{C}\). If \(t_{1}\) and \(t_{2}\) be the distances between them, then
supporting img

1 \(t_{1}=t_{1}\)
2 \(t_{1}>t_{2}\)
3 \(t_{1} < t_{2}\)
4 \(t_{1} \leq t_{2}\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359443 Three concentric metal shells \(A, B\) and \(C\) of respective radii \(a,b\) and \(c\) have surface charge densities \( + \sigma , - \sigma \) and \( + \sigma \) respectively. The potential of shell \(B\) is :

1 \(\frac{\sigma }{{{\varepsilon _0}}}\left[ {\frac{{{a^2} - {b^2}}}{b} + c} \right]\)
2 \(\frac{\sigma }{{{\varepsilon _0}}}\left[ {\frac{{{b^2} - {c^2}}}{b} + a} \right]\)
3 \(\frac{\sigma }{{{\varepsilon _0}}}\left[ {\frac{{{b^2} - {c^2}}}{c} + a} \right]\)
4 \(\frac{\sigma }{{{\varepsilon _0}}}\left[ {\frac{{{a^2} - {b^2}}}{a} + c} \right]\)
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PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359439 Three concentric conducting spherical shells have radii \(r\),\(2r\) and \(3r\) and charges \({q_1},{q_2}\) and \({q_3}\) respectively. The innermost and outermost shells are earthed as shown in the figure. The charges given are after earthing. Select the correct alternative.
supporting img

1 \({q_1} + {q_3} = - {q_2}\)
2 \({q_1} = - {q_2}\)
3 \(\frac{{{q_3}}}{{{q_2}}} = \frac{{ - 1}}{3}\)
4 None of these
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359440 A spherical capacitor is made of two conducting spherical shells of radii \(a\) and \(b\).The space between the shells is filled with a dielectric of dielectric constant \(K\) upto a radius \(b\) as shown in figure. Calculate the capacitance.
supporting img

1 \(\frac{{K4\pi {\varepsilon _0}abc}}{{Ka\left( {c - b} \right) + c\left( {b - a} \right)}}\)
2 \(\frac{{K4\pi {\varepsilon _0}abc}}{{Kab + bc}}\)
3 \(\frac{{K4\pi {\varepsilon _0}abc}}{{{a^2} + {b^2} + {c^2}}}\)
4 None of these
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359441 A small conducting sphere lying concentrically inside a bigger hollow conducting sphere of radius \(R\). The bigger and smaller spheres are charged with \(Q\) and \(q(Q > q)\) and are insulated from each other, The potential difference between the spheres will be

1 \(\frac{1}{{4\pi {\varepsilon _0}}}\left( {\frac{q}{r}\; - \;\frac{Q}{R}} \right)\)
2 \(\frac{1}{{4\pi {\varepsilon _0}}}\left( {\frac{Q}{R}\; + \;\frac{q}{r}} \right)\)
3 \(\frac{1}{{4\pi {\varepsilon _0}}}\left( {\frac{q}{r}\; - \;\frac{q}{R}} \right)\)
4 \(\frac{1}{{4\pi {\varepsilon _0}}}\left( {\frac{q}{R}\; - \;\frac{Q}{r}} \right)\)
KCET - 2008
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359442 Figure shows three spherical and equipotential surfaces \(A, B\) and \(C\) round a point charge \(q\). The potential difference \(V_{A}-V_{B}=V_{B}-V_{C}\). If \(t_{1}\) and \(t_{2}\) be the distances between them, then
supporting img

1 \(t_{1}=t_{1}\)
2 \(t_{1}>t_{2}\)
3 \(t_{1} < t_{2}\)
4 \(t_{1} \leq t_{2}\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359443 Three concentric metal shells \(A, B\) and \(C\) of respective radii \(a,b\) and \(c\) have surface charge densities \( + \sigma , - \sigma \) and \( + \sigma \) respectively. The potential of shell \(B\) is :

1 \(\frac{\sigma }{{{\varepsilon _0}}}\left[ {\frac{{{a^2} - {b^2}}}{b} + c} \right]\)
2 \(\frac{\sigma }{{{\varepsilon _0}}}\left[ {\frac{{{b^2} - {c^2}}}{b} + a} \right]\)
3 \(\frac{\sigma }{{{\varepsilon _0}}}\left[ {\frac{{{b^2} - {c^2}}}{c} + a} \right]\)
4 \(\frac{\sigma }{{{\varepsilon _0}}}\left[ {\frac{{{a^2} - {b^2}}}{a} + c} \right]\)
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PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359439 Three concentric conducting spherical shells have radii \(r\),\(2r\) and \(3r\) and charges \({q_1},{q_2}\) and \({q_3}\) respectively. The innermost and outermost shells are earthed as shown in the figure. The charges given are after earthing. Select the correct alternative.
supporting img

1 \({q_1} + {q_3} = - {q_2}\)
2 \({q_1} = - {q_2}\)
3 \(\frac{{{q_3}}}{{{q_2}}} = \frac{{ - 1}}{3}\)
4 None of these
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359440 A spherical capacitor is made of two conducting spherical shells of radii \(a\) and \(b\).The space between the shells is filled with a dielectric of dielectric constant \(K\) upto a radius \(b\) as shown in figure. Calculate the capacitance.
supporting img

1 \(\frac{{K4\pi {\varepsilon _0}abc}}{{Ka\left( {c - b} \right) + c\left( {b - a} \right)}}\)
2 \(\frac{{K4\pi {\varepsilon _0}abc}}{{Kab + bc}}\)
3 \(\frac{{K4\pi {\varepsilon _0}abc}}{{{a^2} + {b^2} + {c^2}}}\)
4 None of these
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359441 A small conducting sphere lying concentrically inside a bigger hollow conducting sphere of radius \(R\). The bigger and smaller spheres are charged with \(Q\) and \(q(Q > q)\) and are insulated from each other, The potential difference between the spheres will be

1 \(\frac{1}{{4\pi {\varepsilon _0}}}\left( {\frac{q}{r}\; - \;\frac{Q}{R}} \right)\)
2 \(\frac{1}{{4\pi {\varepsilon _0}}}\left( {\frac{Q}{R}\; + \;\frac{q}{r}} \right)\)
3 \(\frac{1}{{4\pi {\varepsilon _0}}}\left( {\frac{q}{r}\; - \;\frac{q}{R}} \right)\)
4 \(\frac{1}{{4\pi {\varepsilon _0}}}\left( {\frac{q}{R}\; - \;\frac{Q}{r}} \right)\)
KCET - 2008
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359442 Figure shows three spherical and equipotential surfaces \(A, B\) and \(C\) round a point charge \(q\). The potential difference \(V_{A}-V_{B}=V_{B}-V_{C}\). If \(t_{1}\) and \(t_{2}\) be the distances between them, then
supporting img

1 \(t_{1}=t_{1}\)
2 \(t_{1}>t_{2}\)
3 \(t_{1} < t_{2}\)
4 \(t_{1} \leq t_{2}\)
PHXII02:ELECTROSTATIC POTENTIAL AND CAPACITANCE

359443 Three concentric metal shells \(A, B\) and \(C\) of respective radii \(a,b\) and \(c\) have surface charge densities \( + \sigma , - \sigma \) and \( + \sigma \) respectively. The potential of shell \(B\) is :

1 \(\frac{\sigma }{{{\varepsilon _0}}}\left[ {\frac{{{a^2} - {b^2}}}{b} + c} \right]\)
2 \(\frac{\sigma }{{{\varepsilon _0}}}\left[ {\frac{{{b^2} - {c^2}}}{b} + a} \right]\)
3 \(\frac{\sigma }{{{\varepsilon _0}}}\left[ {\frac{{{b^2} - {c^2}}}{c} + a} \right]\)
4 \(\frac{\sigma }{{{\varepsilon _0}}}\left[ {\frac{{{a^2} - {b^2}}}{a} + c} \right]\)