An infinite line of charge with linear density 1 6.5 HC/m is positioned along th

Question

An infinite line of charge with linear density 1 6.5 HC/m is positioned along the axis of a thick insulating shell of inner radius a 2.9 cm and outer radius b 4.6 cm. The insulating shell is uniformly charged with a volume density of p- 1) What is 2, the linear charge density of the insulating shell? 2) What is Ex(P), the value of the x-component of the electric field at point P, located a distance 8.6 cm along the y-axis from the line of charge? N/C Sumt 3) What is Ey(P), the value of the y-component of the electric field at point P located a distance 8.6 cm along the y-axis from the line of charge? Sum 4) What is Ex(R), the value of the x-component of the electric field at point R, located a distance 1.45 cm along a line that makes an angle of 30° with the x-axis? Subm 5) What is Ey(R), the value of the y-component of the electric field at point R, located a distance 1.45 cm along a line that makes an angle of 30° with the x-axis? 6) For how many values of r: (2.9 cmr 4.6 cm) is the magnitude of the electric field equal to 0? none one more than one 7) lf we were to double 1 ( 13 C/m), how would E, the magnitude of the electric field at point P, change? E would double E would increase by more than a factor of two E increases by less than a factor of two E decreases by less than a factor of two E decreases by more than a factor of two

Explanation / Answer

1] linear charge density = rho*area = -759*pi*(4.6e-2^2 - 2.9e-2^2) = -3.04 uC/m

2] Ex(P) = 0

It is because the direction of the field will only be in y direction in order to point radially outside the center.

3] Ey(P) = 2k lambda / r = 2*9e9*(6.5e-6 - 3.04e-6)/8.6e-2 = 724186 N/C

4] Ex(R) =  2k lambda / r = 2*9e9*(6.5e-6 )/1.45e-2 = 8068965 N/C

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