Two small insulating spheres with radius 900102m are separat

Two small insulating spheres with radius 9.00×10²m are separated by a large center-to-center distance of 0.485 m . One sphere is negatively charged, with net charge -1.90 C , and the other sphere is positively charged, with net charge 4.10 C . The charge is uniformly distributed within the volume of each sphere.

Part A

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

Take the permittivity of free space to be 0 = 8.85×10¹² C2/(Nm2) .

Part B

What is the direction of the electric field midway between the spheres?

What is the direction of the electric field midway between the spheres?

Solution

Sepoaration of the spheres r = 0.485 m, charge on first sphere q = -1.9* 10^-6 C
charge on second sphere q \' = 4.10 * 10^-6 C.

the magnitude E of the electric field midway between the spheres is
E = E \' + E \"
   = Kq / ( r/ 2)^ 2 + Kq \' / ( r/ 2)^ 2

               = 4K(q+q \') / ( r)^ 2

               = 4*8.99*10^9 *[1.9* 10^-6 + 4.10 * 10^-6] / [ 0.485]^2
               = 9.17e+5 N / C

b,

field lines are starting at positive charge and ending at negative charge.

so, the field is pointed toward the negative sphere.