Two concentric conducting spherical shells of radii a1 and a2 a2 - al are charged to potentials -1 and -2- respectively- Find the charge on the inner shell-

The correct option is A q_1 = 4πε_0 (ϕ_1 ϕ_2/a_2 a_1)a_1a_2 Potential of inner sphere =ϕ_1=14πϵ_o(q_1a_1+q_2a_2) Potential of outer sphere =ϕ_2=14 ...

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Standard XII

Physics

Potential Gradient and Relation between Electric Field and Potential

Two concentri...

Question

Two concentric conducting spherical shells of radii $a_{1}$ and $a_{2} (a_{2} > a_{l})$ are charged to potentials $ϕ_{1}$ and $ϕ_{2}$ , respectively. Find the charge on the inner shell.

q_{1} = 4 π ε_{0} (\frac{ϕ_{1} - ϕ_{2}}{a_{2} - a_{1}}) a_{1} a_{2}

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q_{1} = 4 π ε_{0} (\frac{ϕ_{1} + ϕ_{2}}{a_{2} + a_{1}}) a_{1} a_{2}

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q_{1} = π ε_{0} (\frac{ϕ_{1} - ϕ_{2}}{a_{2} + a_{1}}) a_{1} a_{2}

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q_{1} = 2 π ε_{0} (\frac{ϕ_{1} + ϕ_{2}}{a_{2} - a_{1}}) a_{1} a_{2}

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Solution

The correct option is A $q_{1} = 4 π ε_{0} (\frac{ϕ_{1} - ϕ_{2}}{a_{2} - a_{1}}) a_{1} a_{2}$

Potential of inner sphere $= ϕ_{1} = \frac{1}{4 π ϵ_{o}} (\frac{q_{1}}{a_{1}} + \frac{q_{2}}{a_{2}})$

Potential of outer sphere $= ϕ_{2} = \frac{1}{4 π ϵ_{o}} (\frac{q_{1}}{a_{2}} + \frac{q_{2}}{a_{2}})$

$ϕ_{1} - ϕ_{2} = \frac{1}{4 π ϵ_{o}} (\frac{q_{1}}{a_{1}} - \frac{q_{1}}{a_{2}})$

$⟹ 4 π ϵ_{o} (ϕ_{1} - ϕ_{2}) = q_{1} (\frac{a_{2} - a_{1}}{a_{1} a_{2}})$

$⟹ q_{1} = 4 π ϵ_{o} (\frac{ϕ_{1} - ϕ_{2}}{a_{2} - a_{1}}) a_{1} a_{2}$

Answer-(A)

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Two concentric conducting spherical shells of radii a1 and a2(a2>al) are charged to potentials ϕ1 and ϕ2, respectively. Find the charge on the inner shell.

The correct option is A q1=4πε0(ϕ1−ϕ2a2−a1)a1a2Potential of inner sphere=ϕ1=14πϵo(q1a1+q2a2)Potential of outer sphere=ϕ2=14πϵo(q1a2+q2a2)ϕ1−ϕ2=14πϵo(q1a1−q1a2)⟹4πϵo(ϕ1−ϕ2)=q1(a2−a1a1a2)⟹q1=4πϵo(ϕ1−ϕ2a2−a1)a1a2Answer-(A)

Two concentric conducting spherical shells of radii $a_{1}$ and $a_{2} (a_{2} > a_{l})$ are charged to potentials $ϕ_{1}$ and $ϕ_{2}$ , respectively. Find the charge on the inner shell.