Question

Two small insulating spheres with radius 9.00*10^-2m are separated by a large center-to-center distance of 0.520m . One sphere is negatively charged, with net charge -2.40uC , and the other sphere is positively charged, with net charge 3.35uC . The charge is uniformly distributed within the volume of each sphere.

a)

What is the magnitude E of the electric field midway between the spheres?

Take the permittivity of free space to be ?0 = 8.85

Answer 1

E from both will point the same way

a) E = E1 + E1 = k q/r^1 + k q/r^2 = 9.0E9*(2.4E-6 + 3.35E-6)/(0.52/2)^2= 7.66E5 N/C

b) towards negative sphere

Answer 2

다 Sphese ) Sphere

$\vec E_1 = \frac{kq_1}{r_1^{2}} \hat i$

$\vec E_1 = \frac{9 \times 10 ^9 \times (-2.4) \times 10^{-6}}{0.26^{2}} \hat i = (-319526.63 \hat i ) N /C$

$\vec E_2 =- \frac{kq_2}{r_2^{2}} \hat i$

$\vec E_2 = -\frac{9 \times 10 ^9 \times 3.35 \times 10^{-6}}{0.26^{2}} \hat i = (-446005.92 \hat i ) N /C$

$\vec E_{net} = \vec E_1 + \vec E_2 = -319526.63 - 446005.92 = (-765532.55 \hat i) N/C$

a) Magnitude = 765532.55 N/C

b) Direction towards negative charged sphere

Answer 3

a) The electric field at the mid point will be
Eo = 9x10^9( q1+q2) / d^2, where here d = 0.26 m
so that Eo = 9 x10^9( 2.4+3.35)x10^-6 / 0.0676
= 7.66 x10^5 N/C

b) towards the negatively charged sphere