Question

A 20-cm-radius ball is uniformly charged to 62 nC .

A. What is the ball's uniform charge density (C/m3)?

B. How much charge is enclosed by spheres of radii 5, 10, and 20 cm?

C. What is the electric field strength at points 5, 10, and 20 cm from the center?

Answer 1

given that radius of ball

R = 20 cm = 20*10^-2 m

charge on ball q = 62 nC = 62*10^-9 C

Part (A)

ball's uniform charge density is given by

ρ = Q/V = Total charge /Volume

volume of ball V = 4/3*π*R^3 = 4/3*3.14*(20*10^-2)^3

V = 0.033 m^3

so ρ = 62*10^-9/0.033 = 1.87*10^-6 C/m^3

ρ = 1.87*10^-6 C/m^3

Part(B)

charge enclosed by spheres of radii

for 5 cm

Q5 = ρ*V = 1.87*10^-6*(4/3)*π*(5*10^-2)^3

Q5 = 9.79*10^-10 C

for 10 cm radii

Q10 = ρ*V = 1.87*10^-6*(4/3)*π*(10*10^-2)^3

Q10 = 7.83*10^-9 C

for 20 cm radii

Q20 = ρ*V = 1.87*10^-6*(4/3)*π*(20*10^-2)^3

Q20 = 6.26*10^-8 C

Part(C)

electric field strength at any point is given by

E = kQ/R^2

Electric field strength at point 5 cm from center

E5 = (9*10^9)(62*10^-9)/(5*10^-2)^2

E5 = 223.20*10^3 N/C

Electric field strength at point 10 cm from center

E10 = (9*10^9)(62*10^-9)/(10*10^-2)^2

E10 = 558*10^2 N/C

Electric field strength at point 20 cm from center

E20 = (9*10^9)(62*10^-9)/(20*10^-2)^2

E20 = 139.50*10^2 N/C

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