Question

0/3 points Previous Kat7PSEn 24.Р.029 In Example 24.6, we found that the electric field of a charged disk approaches that of a charged particle for distances y that are large compared to R, the radius of the disk. To see a numerical instance of this, calculate the magnitude of the electric field a distance y 3.1 m from a disk of radius R 3.1 cm that has a total charge of 7.0 μC using the exact formula as follows. (Enter your answer to at least one decimal place.) x N/C Then alcu ale ㎞em nitude of tre eletriched at y- least one decimal place.) m, assuming that the disk is a partic e or the same total charge at the origin. Enter your answer to at N/C Compare your answers. (Assume the two answers are close if they are within 5% of each other.) 1.1 The two answers are very different. The two answers are close Practice Another Version

Answer 1

given

equation

E = 2 $\pi$ k $\sigma$ ( 1 - y / ( y² + R² )^1/2 )

and

R = 3.1 cm

= 0.031 m

y = 3.1 m

Q = 7 uC

= 7 x 10^-6 C

area A = $\pi$ R²

= 3.14 x 0.031²

A = 3.0175 x 10^-3 m²

using equation for $\sigma$ is

$\sigma$ = Q / A

= 7 x 10^-6 / 3.0175 x 10^-3

$\sigma$ = 2.32 x 10^-3 C/m²

so finally

E = 2 x 3.14 x 9 x 10⁹ x 2.32 x 10^-3 ( 1 - 3.1 / ( 3.1² + 0.031² )^1/2 )

E = 6555.8283 N/C

we cannot say very close or different that without example 24.6.