(a) A charge of -290e is uniformly distributed along a circular arc of radius 4.

Question

(a) A charge of -290e is uniformly distributed along a circular arc of radius 4.15 cm, which subtends an angle of 40°. What is the linear charge density along the arc?
__________ C/m

(b) A charge of -290e is uniformly distributed over one face of a circular disk of radius 2.20 cm. What is the surface charge density over that face?
_____________ C/m2

(c) A charge of -290e is uniformly distributed over the surface of a sphere of radius 2.20 cm. What is the surface charge density over that surface?
_____________ C/m2

(d) A charge of -290e is uniformly spread through the volume of a sphere of radius 2.20 cm. What is the volume charge density in that sphere?
______________ C/m3

Explanation / Answer

charge q =-290 e =-290*1.602*10^-19 C

1)

radius of arc r =4.15 cm =4.15*10^-2 m
angle =40 deg =40*2/360 =0.698 rad

so ,the arc length L =r =(4.15*10^-2)(0.698) =0.0289 m

linear charge density =q/L = -1.6*10^-15 C/m

2)

radius of circular disk r =  2.20 cm =2.2*10^-2 m

surface charge density =q/A =q/r^2 = -3.059*10^-14 C/m^2

3)

radius of sphere r =  2.20 cm =2.2*10^-2 m

surface charge density =q/A =q/4r^2 = -7.64*10^-15 C/m^2

4)

radius of sphere r =  2.20 cm =2.2*10^-2 m

volume of a sphere V =(4/3)r^3

charge density =q/V =(q)/[(4/3)r^3] = -1.853*10^-12 C/m^3

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