A metal sphere hangs from a string and has 2 kg of mass. The sphere has a charge of +7.1 µC. A uniform electric field is turned on and directed to the right.

and....?

To determine the motion of the metal sphere in the given scenario, we need to consider two forces acting on it: the gravitational force and the electrostatic force.

1. Gravitational Force:
The gravitational force acting on the sphere can be calculated using the equation: F_gravity = m * g, where m is the mass of the sphere and g is the acceleration due to gravity (approximately 9.8 m/s^2 on Earth). In this case, the mass of the sphere is given as 2 kg, so the gravitational force is: F_gravity = 2 kg * 9.8 m/s^2 = 19.6 N.

2. Electrostatic Force:
The electrostatic force acting on the sphere can be calculated using the equation: F_electric = q * E, where q is the charge on the sphere and E is the electric field strength. In this case, the charge on the sphere is given as +7.1 µC (microcoulombs) and the electric field is directed to the right. However, the magnitude of the electric field is not mentioned, so we cannot calculate the electrostatic force without that information.

Once the magnitudes of both the gravitational force and the electrostatic force are determined, we can compare them to predict the motion of the metal sphere. If the electrostatic force is greater, the sphere will move to the right due to the net force in that direction. If the gravitational force is greater, the sphere will move downward.

Therefore, to fully analyze the situation and determine the motion of the metal sphere, we need to know the magnitude of the electric field strength (E).