A point charge q 1 = -5.8 C is located at the center of a thick conducting shell

Question

A point charge q1 = -5.8 C is located at the center of a thick conducting shell of inner radius a = 2.9 cm and outer radius b = 4.5 cm, The conducting shell has a net charge of q2 = 1.8 C.

1)

What is Ex(P), the value of the x-component of the electric field at point P, located a distance 6.3 cm along the x-axis from q1?N/C

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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 6.3 cm along the x-axis from q1?N/C

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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 1.45 cm along the y-axis from q1?N/C

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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 1.45 cm along the y-axis from q1?N/C

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5)

What is b, the surface charge density at the outer edge of the shell?C/m2

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6)

What is a, the surface charge density at the inner edge of the shell?C/m2

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Explanation / Answer

1) Ex(P) = k*(q1+q2)/rp^2

= 9*10^9*(-5.8+1.8)*10^-6/0.063^2

= -9.07*10^6 N/c (towards -x axis)

2) Ey(p) = 0

3) Ex(R) = 0

4) Ex(y) = k*q1/R^2

= 9*10^9*(-5.8)*10^-6/0.0145^2

= -2.48*10^8 N/c (towards -y axis)

5) charge on outer surface, qb = (-5.8+1.8)*10^-6

= -4*10^-6 C

so, sigma_b = qb/(4*pi*b^2)

= -4*10^-6/(4*pi*0.045^2)

= -1.57*10^-4 C/m^2

6) qa = +5.8*10^-6 C

sigma_a = qa/(4*pi*a^2)

= -4*10^-6/(4*pi*0.029^2)

= -3.78*10^-4 C/m^2

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