Question

A uniformly charged, straight filament 3.60 m in length has a total positive charge of 2.00 µC. An uncharged cardboard cylinder 4.30 cm in length and 10.0 cm in radius surrounds the filament at its center, with the filament as the axis of the cylinder.

(a) Using reasonable approximations, find the electric field at the surface of the cylinder.

magnitude	Does the presence of the cardboard tube affect the electric field at its surface? kN/C
direction	---Select--- radially outward radially inward or outward

(b) Using reasonable approximations, find the total electric flux through the cylinder.

Is there a significant amount of flux through the ends of the cardboard tube? N · m²/C

Answer 1

a)

Q = total charge on the filament = 2 µC = 2 x 10^-6 C

L = length of filament = 3.60 m

Linear charge density of the filament is given as

= Q/L = (2 x 10^-6)/3.60 = 5.6 x 10^-7 C/m

r = radius of the cylinder = 10 cm = 0.10 m

Electric field at the surface is given as

E = 2 k /r

E = 2 (9 x 10⁹) (5.6 x 10^-7 )/0.10

E = 1.008 x 10⁵ N/C

b)

A = curved surface area of the cylinder

l = length of cylinder = 4.30 cm = 0.043 m

curved surface area of the cylinder is given as

A = 2rl = 2 (3.14) (0.10) (0.043) = 0.027 m²

Electric flux is given as

= E A

= (1.008 x 10⁵) (0.027)

= 2.7 x 10³ Nm²/C