Question

Answers I've tried that do not work: 5.6%, 5.5%, 4.4%, 4.3%

for E_point i get 1.8 and E_disk i get 1.72

NOTE: Final answer is rounded to two significant-figures

Answer 1

given

R = 2.5 cm

= 0.025 m

Q = 2 x 10^-12

$\sigma$ = Q / 3.14 R²

= 2 x 10^-12 / 3.14 x 0.025²

$\sigma$ = 1.0191 x 10^-9 C/m²

x = 10 cm

= 0.1 m

using equation for E_disk = ( $\sigma$/2$\varepsilon$_o ) ( 1 - 1 / ( ( R²/x²) + 1 )^1/2 )

= ( 1.0191 x 10^-9 / 2 x 8.85 x 10^-12 ) ( 1 - ( ( 0.025²/0.1²) + 1 )^1/2 )

= 57.576 x 0.029857

E_disk = 1.719 N/C

and

E_point = k Q / x²

= 9 x 10⁹ x 2 x 10^-12 / 0.1²

E_point = 1.8

%$\Delta$E = ( E_point - E_disk ) x 100 / E_point

= ( 1.8 - 1.719 ) x 100 / 1.8

%$\Delta$E = 4.50 %