(a) A charge of -310 e isuniformly distributed along a circular arc of radius 4.

Question

(a) A charge of -310e isuniformly distributed along a circular arc of radius 4.20 cm, which subtends an angle of 41°. What is thelinear charge density along the arc?
1 C/m

(b) A charge of -310e isuniformly distributed over one face of a circular disk of radius2.00 cm. What is the surface chargedensity over that face?
2 C/m2

(c) A charge of -310e isuniformly distributed over the surface of a sphere of radius2.00 cm. What is the surface chargedensity over that surface?
3 C/m2

(d) A charge of -310e isuniformly spread through the volume of a sphere of radius2.00 cm. What is the volume chargedensity in that sphere?
4 C/m3

Section 22-6 The Electric Field Due to a Lineof Charge
Section 22-6 The Electric Field Due to a Lineof Charge

Explanation / Answer

(a) length of line = 2r *41/360 = 2 * 4.20 * 41/360 = 3.005464 cm .     charge density = -310*1.60 x10-19 / 0.03005464 =     -1.65 x10-15 C/m . (b)    area = r2 = * 0.022 =    0.0012566 m2 .     charge density = -310*1.60 x10-19 / 0.0012566 =    -3.95 x10-14 C/m2 . (c)   area = 4r2 = 4 * 0.022 = 0.0050266m2 .      charge density = -310*1.60 x 10-19 / 0.0050266  =    -9.87 x 10-15 C/m2 . (d)   volume = (4/3) r3 = (4/3) * 0.023 =    3.351 x 10-5 m3 .     charge density = -310*1.60 x10-19 / 3.351 x 10-5=    -1.48 x10-12 C/m3 .     charge density = -310*1.60 x10-19 / 3.351 x 10-5=    -1.48 x10-12 C/m3

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