Final answer:
To calculate the initial speed, we can use the conservation of energy. The speed is halved when the distance is quadrupled. To find the acceleration at the turning point, use the equation F = ma.
Step-by-step explanation:
To calculate the initial speed of the electron, we can use the conservation of energy. The potential energy of the electron at a distance of 0.33 mm from the surface of the sphere is equal to the kinetic energy it had when it reached that point. We can use the formula for electric potential energy, U = kQq/r, where k is the Coulomb constant, Q is the charge of the sphere, q is the charge of the electron, and r is the distance between the charges. For part (b), we can use the equation for kinetic energy, K = (1/2)mv², where m is the mass of the electron and v is its velocity. Solving for r in terms of v, we find that the distance from the surface of the sphere is proportional to the square of v. Therefore, when the electron's velocity is halved, the distance from the surface of the sphere will be quadrupled. To calculate the acceleration of the electron at its turning point, we can use the equation F = ma, where F is the electric force between the sphere and the electron, m is the mass of the electron, and a is the acceleration.