Question 597: Electrostats & Capacitance

Question

A charge Q is distributed over three concentric spherical shells of radii a, b, c (a < b < c) such that their surface charge densities are equal to one another. The total potential at a point at distance r from their common centre, where r < a, would be -

Accepted Answer

Potential at point P,  V = $${{k{Q_a}} \over a} + {{k{Q_b}} \over b} + {{k{Q_c}} \over c}$$
$$ \because $$  Q
a
: Q
b
: Q
c
: : a
2
: b
2
: c
2
{since  $$\sigma $$
a
= $$\sigma $$
b
= $$\sigma $$
c
}
$$ 	herefore $$  Q
a
= $$\left[ {{{{a^2}} \over {{a^2} + {b^2} + {c^2}}}} ight]$$Q
Q
b
= $$\left[ {{{{b^2}} \over {{a^2} + {b^2} + {c^2}}}} ight]$$ Q
Q
c
= $$\left[ {{{{c^2}} \over {{a^2} + {b^2} + {c^2}}}} ight]$$ Q
V = $${Q \over {4\pi { \in _0}}}\left[ {{{\left( {a + b + c} ight)} \over {{a^2} + {b^2} + {c^2}}}} ight]$$

Answer

$${{Q\left( {{a^2} + {b^2} + {c^2}} \right)} \over {4\pi {\varepsilon _0}\left( {{a^3} + {b^3} + {c^3}} \right)}}$$

Answer

$${Q \over {4\pi {\varepsilon _0}\left( {a + b + c} \right)}}$$

Answer

$${Q \over {12\pi {\varepsilon _0}}}{{ab + bc + ca} \over {abc}}$$

Answer

$${{Q\left( {a + b + c} \right)} \over {4\pi {\varepsilon _0}\left( {{a^2} + {b^2} + {c^2}} \right)}}$$

Electrostats & Capacitance

A charge Q is distributed over three concentric spherical shells of radii a, b, c (a < b < c) such that their surface charge densities are equal to one another. The total potential at a point at distance r from their common centre, where r < a, would be -

Choose the correct answer: