a) A long straight metal wire of radius r1= 3.50E-2 m is surrounded by a metalic

Question

a) A long straight metal wire of radius r1= 3.50E-2 m is surrounded by a metalic cylindrical shell of inner radius r2= 1.40E-1 m and outter radius r3= 1.84E-1 m. The axes of the wire and the cylindrical shell coincide. The wire carries a charge per unit length 3.10E-6 C/m and the shell carries a charge per unit length -6.20E-6 C/m.

Find the magnitude of the electrical field at a position p1= 8.40E-2 m?

b) Find the magnitude of the electrical field at a position p2= 1.58E-1 m?


c) Find the magnitude of the electrical field at a position p3= 2.49E-1 m?

Explanation / Answer

We need to construct appropriate Gaussian surface for the charged cylinder.

For the first case, the point is in between the charged cylinder and metal wire so the field is only due to the metal wire.

Electric field due to a cylinder is E = (charge/length)/(Epsilon_0*2*pi*R)
E = 6.70E-6 /(9*10^12 * 2*3.14*.076) = 6.7/(9*2*3.14*0.076)*10^-18 =1.55 10^-18

a)For a point in between the cylindrical shell and a point inside the shell
Charge density of the cylinder is
rho = -1.34E-5 /(pi*(.187^2 - .1^2)) = -17.08259 E-5

So at this point which is in between the cylinder.
E = (-17.08259 E-5 *pi*(.163^2-.1^2) + 6.70E-6)/(Epsilon_0*2*pi*.163)
= (- 8.892E-6 + 6.70E-6)(Epsilon_0*2*pi*.163) = -2.192/(9*2*3.14*.163) E-18 = -0.2379 E-18

b) for the point completely outside the surfaces
E = (6.7 - 13.4 E-6) /(Epsilon_0*2*pi*.233) = - 6.7 /(9*2*pi*.233) E-18 = -0.508E-18

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