An infinite line of charge with linear density ? 1 = 8.5 ?C/m is positioned alon
ID: 1276389 • Letter: A
Question
An infinite line of charge with linear density ?1 = 8.5 ?C/m is positioned along the axis of a thick insulating shell of inner radius a = 2.3 cm and outer radius b = 4.9 cm. The insulating shell is uniformly charged with a volume density of ? = -779 ?C/m3
1) What is Ey(P), the value of the y-component of the electric field at point P, located a distance 7.8 cm along the y-axis from the line of charge?
2) What is Ex(R), the value of the x-component of the electric field at point R, located a distance 1.15 cm along a line that makes an angle of 30o with the x-axis?
3) What is Ey(R), the value of the y-component of the electric field at point R, located a distance 1.15 cm along a line that makes an angle of 30o with the x-axis?
Explanation / Answer
-779 * area = -779 * pi * (0.0492 - 0.0232)
= -4.58 muC/m
lamba = 8.5 - 4.58 = 3.92 muC/m
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Ey = lambda / (2 pi e_0 r)
= 3.92 * 10-6 / (2 * pi * 8.85 * 10-12 * 7.8 * 10-2)
= 9.03 * 105 N/C
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only for inner wire lambda = 8.5 muC
Ex = E cos 30 = 8.5 * 10-6 / (2 * pi * 8.85 * 10-12 * 1.15 * 10-2) * cos(30)
= 11.5 * 106 N/C
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Ey = E sin (30) =8.5 * 10-6 / (2 * pi * 8.85 * 10-12 * 1.15 * 10-2) * sin (30)
= 6.65 * 106 N/C