Question

A solid sphere of radius 30cm is uniformly charged to 100nC. a) What is the volume charge density of the sphere? b) What is the strength of the E-field at r-10cm, r-20cm, and r-30cm

Answer 1

given,

total charge Q = 100 n C

= 100 × 10⁻⁹ C

radius of the solid sphere = 30 cm

= 0.3 m

Volume of sphere =
`(4)/(3)\pi r^3`

=
`(4)/(3)\pi* 0.3^3`

=0.113 m³

a) volume charge density

`\rho = (10^(-7))/(0.133)`

ρ = 8.85 × 10⁻⁷ C/m³

b) at r = 10 cm = 0.1 m

charge in the sphere at radius

`Q = (4)/(3)\pi* 0.1^3\time \rho`

= 3.7037 \times 10^{-9}C[/tex]

Field strength

`E_1 = (Q)/(4\pi \epsilon_0 r^2)`

`E_1 = (3.7037 * 10^(-9))/(4\pi * 8.85* 10^(-12)* 0.1^2)`

=
`3.33 * 10^3 N/C`

at r = 20 cm = 0.2 m

`Q = (4)/(3)\pi* r^3\time \rho`

`E_1 = (Q)/(4\pi \epsilon_0 r^2)`

`E_1 = ( (4)/(3)\pi* r^3\time \rho)/(4\pi \epsilon_0 r^2)`

`E_1 = (\rho)/(3 \epsilon_0)`

`E_1 = (0.2* 8.842 * 10^(-7))/(3 * 8.85* 10^(-12))`

=
`6.66 * 10^3 N/C`

at r = 30 cm

`E_1 = (\rho)/(3 \epsilon_0)`

`E_1 = (0.3* 8.842 * 10^(-7))/(3 * 8.85* 10^(-12))`

= 9.99 N/C