Use the step-by-step approach in Problem 60 to find the electric field produced by the hollow metal cylinder with charge per unit length λ = 1.0 × 10^-6 C/m in Figure P17.61. Be sure to find the electric fields inside and outside the cylinder, assuming you are far from the ends and that the cylinder is extremely long.

Figure P17.61

Data From Problem 60

Consider a very long, very thin plastic rod as sketched in Figure P17.60. Assume the rod has length L = 1.0 × 10⁶ m and a total charge of 1.0 C distributed evenly along the rod. Your job in this problem is to calculate the electric field a distance r = 10 cm from the rod. 

(a) What is the direction of the electric field? Give a qualitative answer. Is the field directed toward or away from the rod? 

(b) What Gaussian surface matches the symmetry of this problem? Can you pick a surface on which the electric field is constant and perpendicular to the surface or zero at all points on the surface? 

(c) What is the total charge inside your Gaussian surface? 

(d) Use Gauss’s law to find the electric field.

Figure P17.60

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