Question

An electrostatic paint sprayer has a 0.350 m diameter metal sphere at a potential of 26.0 kV. (a) What charge is on the sphere? с (b) Paint droplets initially at rest are dispensed from a paint gun. These droplets are then repelled by the paint sprayer toward the object to be painted. This object is grounded and therefore the electric potential is taken to be zero everywhere on the object. What charge must a 0.400 mg drop of paint have to arrive at the grounded object with a speed of 11.0 m/s? с

Answer 1

The charge on the metal sphere is found using the formula Q = Vr/k. The charge needed for a paint droplet to achieve the specified speed is determined by equating the kinetic energy to the initial electrical potential energy and solving for q.

Step-by-step explanation:

Electrostatic Paint Sprayer Charge Calculation

To calculate the charge on the sphere (a), we can use the formula for the potential (V) of a conducting sphere, which is V = kQ/r, where V is the potential, k is the Coulomb's constant (8.99 × 10^9 Nm^2/C^2), Q is the charge, and r is the radius of the sphere. Since we have the diameter, we can divide it by two to find r, and then rearrange the formula to solve for Q: Q = Vr/k.

To determine the charge that must be on a paint droplet (b) to arrive at the grounded object with a specified speed, we can set the kinetic energy (KE) of the paint droplet equal to the electrical potential energy (PE) that it had before being accelerated. The kinetic energy is given by KE = 0.5mv^2, where m is the mass and v is the velocity. The potential energy can be expressed as PE = qV, where q is the charge on the droplet and V is the potential. Because we are considering the grounded object as a reference point with zero potential, the potential energy initially is q * 26.0 kV. Setting KE equal to PE and solving for q, we find q = (0.5mv^2)/V.