Practice with charge densities Please state your answers to the questions below

Question

Practice with charge densities Please state your answers to the questions below using the same notation as presented in class and the proper number of significant figures: a) A charge of -30 mu C is uniformly distributed along a circular arc of radius 4.00 cm, which subtends an angle of 40 degree. What is the linear charge density along the arc? b) A charge of -30 mu C is uniformly distributed over one face of a circular disk of radius 2.00 cm. What is the surface charge density over that face? c) A charge of -30 mu C is uniformly distributed over the surface of a sphere of radius 2.00 cm. What is the surface charge density over that surface? d) A charge of -30 mu C is uniformly distributed through the volume of a sphere of radius 2.00 cm. What is the volume charge density in that sphere?

Explanation / Answer

(a) Q = - 30 uC = - 30 x 10-6 C R = 4 cm = 0.04 m

so the length of circle = 2 x 3.14 x R

= 2 x 3.14 x 0.04 = 0.2512 m

so the length of arc = ( 40 / 360 ) x length of circle

L = 0.02791 m

so the charge density = Q / L

= ( - 30 x 10-6 ) / 0.02791

= - 1074.840 x 10-6 C/m Ans

(b) here R = 2 cm = 0.02 m

so the surface cahrge density

= Q / A

= ( -30 x 10-6 ) / ( 3.14 x 0.02 x 0.02 )

= - 23855.350 x 10-6  C/m2   Ans

(c) R = 2 cm = 0.02 m

area of sphere = 4 x 3.14 x 0.02 x 0.02

A = 0.005024 m2

so the surface charge density

= Q / A

= ( -30 x 10-6 ) / 0.005024

= - 5971.337 x 10-6 C/m2   Ans

(d) R = 2 cm = 0.02 m

volume of sphere V = (4/3) x pi x R3

= (4/3) x 3.14 x (0.02)3

= 0.000033493 m3

so the volume charge density

= Q / V

= ( -30 x 10-6 ) / 0.000033493

= - 895700.6369 x 10-6   C/m3   Ans

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