Question

Two small metallic spheres, each of mass m = 0.214 g, are suspended as pendulums by light strings of length L as shown in the figure below. The spheres are given the same electric charge of 7.3 nC, and they come to equilibrium when each string is at an angle of ? = 4.80° with the vertical.

Answer 1

Given

mass of each sphere m = 0.214 g

charge on each sphere q = 7.3 n C = 7.3*10^-9 C

θ = 4.80 degrees

The sphere is in equillibrium under the application of force T from the string , the electric force From the other spring and gravitational force

    F_x = T sinθ - F = 0

               F = T sin θ ......(1)

      Fy = T cosθ - mg = 0

               T cosθ = mg   ......(2)

      From equations (1) and (2)

      tanθ = F / mg

           F = mg tan θ

using geometry of rightangle triangle

            sin θ = a / L

            a = L sin θ  

Force between two charges is

           F = k q ² / r ²  

          mg tan θ     = ( 9*10⁹)(7.3*10^-9 C)² / ( 2a)²  

           ( 0.214*10^-3 kg ) ( 9.8 )tan ( 4.8) = ( 9*10⁹)(7.3*10^-9 C)² / ( 2a)²  

                 a =   0.026

              L sin θ = 0.026

                   L = 0.311m