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30 March, 05:58

A uniformly charged ball of radius a and charge? Q is at the center of a hollow metal shell with inner radius b and outer radius c. The hollow sphere has net charge + 2Q.

Part A

Determine the electric field strength in the region r? a. Give your answer as a multiple of Q/?0.

Express your answer in terms of some or all of the variables a, b, c, r, and the constant?.

Park B

Determine the electric field strength in the region a

Express your answer in terms of some or all of the variables a, b, c, r, and the constant?.

Part C

Determine the electric field strength in the region b

Part D

Determine the electric field strength in the region c

Express your answer in terms of some or all of the variables a, b, c, r, and the constant?.

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Answers (1)
  1. 30 March, 09:16
    0
    A) E = 1/4π ε₀ r/3a³, B) E = 1/4πε₀ Q / r²

    , C) E = 0

    , D) E = 1/4πε₀ 3Q / r²

    Explanation:

    For this exercise let's use Gauss's law

    Ф = ∫ E. dA = / ε₀

    Since the two objects are spherical we will use a sphere as our Gaussian surface

    E A = q_{int} / ε₀

    E 4π r² = q_{int} / ε₀

    Part A

    The radius is r
    In this case the chage inside of the Gaussian surface can be found using the concept of density

    ρ = q / V

    q_{int} = ρ 4/3 π r³

    We replace

    E 4π r² = rho 4/3 π r³ 1/ε₀

    E = rho r/3ε₀

    E = 1/4π ε₀ r/3a³ r
    Part B

    In this case they ask for the field between the sphere and the shell

    a
    In this case the charge inside is the charge of the sphere, we replace

    E (4π r²) = Q / ε₀

    E = 1 / 4πε₀ Q / r²

    Part C

    The electric filed in the region inside the spherical shell

    b
    An electric conductor in equilibrium all the charge is on its surface so the charge inside the conductor is zero

    q_{int} = 0

    E = 0

    Part D

    In the region outside ofthe hollow shell

    c
    The charge inside is

    q_{int} = Q + 2Q = 3 Q

    The electric field is

    E = 1 / 4πε₀ 3Q / r²
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