Final answer:
The angle that the silk string makes with the vertical can be determined using the concept of equilibrium. By setting the forces of tension, gravity, and the electric field equal to each other, we can solve for the angle. Plugging in the given values, the angle is approximately 62.9 degrees.
Step-by-step explanation:
The angle that the silk string makes with the vertical can be determined using the concept of equilibrium. The force of the tension in the string, T, is equal to the force of gravity acting on the sphere, mg, and the force of the electric field due to the conducting plate, E. The electric field can be calculated using the equation E = σ/ε₀, where σ is the charge density of the conducting plate and ε₀ is the absolute permittivity of free space. By setting these forces equal to each other and solving for the angle, we can find that the angle is given by the equation tanθ = mg/E.
Plugging in the values, we can calculate the angle to be approximately 62.9 degrees.