(a) A charge of -330 e is uniformly distributed along a circular arc of radius 4
ID: 1434218 • Letter: #
Question
(a) A charge of -330e is uniformly distributed along a circular arc of radius 4.10 cm, which subtends an angle of 40°. What is the linear charge density along the arc?
C/m
(b) A charge of -330e is uniformly distributed over one face of a circular disk of radius 1.90 cm. What is the surface charge density over that face?
C/m2
(c) A charge of -330e is uniformly distributed over the surface of a sphere of radius 1.90 cm. What is the surface charge density over that surface?
C/m2
(d) A charge of -330e is uniformly spread through the volume of a sphere of radius 1.90 cm. What is the volume charge density in that sphere?
C/m3
Explanation / Answer
Charge Q = - 330 e = 330 * 1.6 * 10-19 C
= - 528 * 10-19 C
1)Radius of the circular arc R = 4.1 cm = 4.1 * 10-2 m
Angle = 400
= 40 * / 180
= 0.697 rad
so the length of the arc is l = 4.1 * 10-2 * 0.697
= 2.86 * 10-2 m
Then the linear charge density is given by
= charge / length
= 528 * 10-19 / 2.86 * 10-2
= 184.6 * 10-17 C / m
2) Radius of the disk r = 1.90 cm
= 1.90 * 10-2 m
Now area of the disk A = * r2 = 3.14 * ( 1.9 * 10-2 )2
= 11.33 * 10-4 m2
Now surface charge density = Q / A
= 528 * 10-19 / ( 11.33 * 10-4 )
= 46.60 * 10-15 C / m2
3)Radius of the sphere r = 1.9 cm = 1.9 * 10-2 m
Area of the sphere A = 4 * * r2
= 4 * 3.14* (1.9 * 10-2 )2
= 45.32 * 10-4 m2
Now surface charge density = Q / A
= 528 * 10-19 / ( 45.32 * 10-4 )
= 11.65 * 10-15 C / m2
4)Volume of the sphere V = 4 * * r3
= 4 * 3.14 * ( 1.9 * 10-2 )3
= 86.14 * 10-6 m3
Now the volume charge density = Q / V
= ( 528 * 10-19 ) / ( 86.14 * 10-6 )
= 6.13 * 10-13 C / m3
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