A point charge q1 = -7.2 μC is located at the center of a thick conducting shell of inner radius a = 2.4 ?

A point charge q1 = -7.2 μC is located at the center of a thick conducting shell of inner radius a = 2.4 cm and outer radius b = 4.8 cm, The conducting shell has a net charge of q2 = 2.9 μC.

1)What is Ex(P), the value of the x-component of the electric field at point P, located a distance 6.7 cm along the x-axis from q1?N/C 2)What is Ey(P), the value of the y-component of the electric field at point P, located a distance 6.7 cm along the x-axis from q1?N/C 3)What is Ex(R), the value of the x-component of the electric field at point R, located a distance 1.2 cm along the y-axis from q1?N/C 4)What is Ey(R), the value of the y-component of the electric field at point R, located a distance 1.2 cm along the y-axis from q1?N/C 5)What is σb, the surface charge density at the outer edge of the shell? C/m^2 6)What is σa, the surface charge density at the inner edge of the shell?

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  • 4 weeks ago

    Draw a diagram.  You will have a hollow shell with q1 in the centre of the hollow, which I assume is the origin (0,0).

    The ‘total’ charge enclosed by any conductor appears on the conductor’s outer surface.

    Inside a conductor (including cavities) the field is zero.

    The system’s total charge is Q = q1+q2=(-7.2+2.4)  μC = -4.8μC.  This is the charge on the *outer surface of the shell*.

    The charge on the inner surface of the shell is -q1 = +7.2μC.

    Here’s the method.

    ________________

    1) What is Ex(P), the value of the x-component of the electric field at point P, located a distance 6.7 cm along the x-axis from q1?N/C

    P is outside the shell and the system is spherically symmetric so the field is the same as from a point charge.  Ex(P) = kQ/r² where Q is the total charge (see above) and r = 0.067m.

    (k = 1/(4πε₀) so we can also write the equation as Ex(P) = Q/(4πε₀r²))

    You can also do this using Gauss’s law.  E.g. question 3).

    __________________

    2) What is Ey(P), the value of the y-component of the electric field at point P, located a distance 6.7 cm along the x-axis from q1?N/C

    Same as 1) because of the spherical symmetry.

    ________________

    3) What is Ex(R), the value of the x-component of the electric field at point R, located a distance 1.2 cm along the y-axis from q1?N/C

    1.2cm gives point R inside the hollow.   The field at 1.2cm is due only to q1 so Ex(R) = kq1/r² where r = 0.012m

    If preferred, use a spherical Gaussian surface centred on q1, radius 1.2m.  Then use Gauss’s law and symmetry to give:

    4πr²Ex(R) = q1/ε₀

    ________________

    4) What is Ey(R), the value of the y-component of the electric field at point R, located a distance 1.2 cm along the y-axis from q1?N/C

    Same as 3).

    ________________

    5) What is σb, the surface charge density at the outer edge [surface] of the shell? C/m^2

    Divide Q by outer surface area.

    _____________________

    6) What is σa, the surface charge density at the inner edge [surface]? C/m^2

    Divide -q1 by the inner surface area.

  • 4 weeks ago

    I don't believe that a point charge can exist within the thickness of a conductor.

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