# 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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• 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.

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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).

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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.

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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

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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).

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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.

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

Divide -q1 by the inner surface area.

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