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Using Gauss's law derive an expression f...

Using Gauss's law derive an expression for the electric field at any point outside a uniformaly charged thin spherical shell of radius R and charge density `sigma C//m^(2) `. Draw the field lines when the charges density of the sphere is (i) positive (ii) negative.
(b) A uniformly charged conducting sphere of 2.5 m in diameter has a surface charge density of `100 mu C //m^(2) ` Calculate the
(i) charge on the sphere (ii) total electric flux passing through the sphere.

Text Solution

Verified by Experts

As diameter D = 2.5 m , hence radius R = ` (D)/( 2) = 1.25 m `
(i) ` therefore ` Total charge on the sphere `Q= sigma . 4 pi R^(2) =(100 muC// m^(2)) xx 4 pi xx ( 1.25) ^(2) m^(2) = 1.96 xx 10 ^(3) C `
(ii) Total electric flux through the sphere
` " " phi_in =(1)/( in_0) ,(Q) =( 1.96 xx 10 ^(-3))/( 8.85 xx 10 ^(-12)) = 2.2 xx 10 ^(8) V. m `
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(a) Using Gauss's law, derive an expression for the electric field intensity at any point outside a uniformly charged thin spherical shell of radius R and charge density sigma C//m^(2) . Draw the field lines when the charge density of the sphere is (i) positive, (ii) negative. (b) A uniformly charged conducting sphere of 2.5 m in diameter has a surface charge density of 100 mu C//m^(2) . Calculate the (i) charge on the sphere (ii) total electric flux passing through the sphere.

Using Gauss's theorem derive an expression for the electric field at any point outside a charged spherical shell of radius R and of charge density sigma C//m^(2)

Knowledge Check

  • A uniformly charged conducting sphere of 4.4 m diameter has a surface change density of 60muCm^(-2) . The charge on the sphere is

    A
    `7.3xx10^(-3)C`
    B
    `3.7xx10^(-6)C`
    C
    `7.3xx10^(-6)C`
    D
    `3.7xx10^(-3)C`

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