Question

A metal sphere hangs from a string and has 2 kg of mass. The sphere has a charge of +5.5

Answer 1

given that :

mass of the sphere, m = 2 kg

charge on the sphere, q = 5.5 C = 5.5 x 10^-6 C

(b) the electric force on the metal sphere is given as ::

F_e = q E                             { eq. 1 }

where, E = electric field = 10⁶ N/C

inserting the values in above eq.

F_e = (5.5 x 10^-6 C) (10⁶ N/C)

F_e = 5.5 N

(c) when the sphere reaches equilibrium, then it makes an angle with the vertical axis which is given as :

the electric force act horizontally and the gravitational force act vertically, it means that the sum of both forces can never be zero.

tan = y / x                               { eq. 1 }

where, y denotes for electric force F_e

x denotes for gravitational force F_g

F_g = mg = (2 kg) (9.8 m/s²) = 19.6 N

inserting the values in eq.2,

tan = y / x = F_e / F_g

= tan^-1 (5.5 / 19.6)

= tan^-1 (0.2806)

= 15.6 degree