Electrons are continually being knocked out of air molecules in the atmosphere by cosmic-ray particles coming in from space. Once released, each electron experiences an electric force F due to the electric field É that is produced in the atmosphere by charged particles already on Earth. An electric field Ē with an average magnitude of about 150 N/C points downward in the atmosphere near Earth's surface, where a friendly bat named Gerald (pictured below) is flitting about, navigating via ultrasonic bleeps. To give Gerald some company, we wish to "float" a sulfur (S, with mass density ps ~ 2.1 × 10³ kg/m³) sphere weighing 4.4 N in this field by charging the sphere. (a) What charge (both sign and magnitude) must be used? (b) Why is this experiment impractical? Please give a quantitative answer. Hint: Humid air has a dielectric (breakdown) strength of × 3.0 × 10€ N/C. (c) What is the change AU in the electric potential energy of a released electron when the electric force causes it to move vertically upward through a distance d 520 m? (d) Through what potential change does the electron move?

Electrons are continually being knocked out of air molecules in the atmosphere by cosmic-ray particles coming in from space. Once released, each electron experiences an electric force F due to the electric field É that is produced in the atmosphere by charged particles already on Earth. An electric field Ē with an average magnitude of about 150 N/C points downward in the atmosphere near Earth's surface, where a friendly bat named Gerald (pictured below) is flitting about, navigating via ultrasonic bleeps. To give Gerald some company, we wish to "float" a sulfur (S, with mass density ps ~ 2.1 × 10³ kg/m³) sphere weighing 4.4 N in this field by charging the sphere. (a) What charge (both sign and magnitude) must be used? (b) Why is this experiment impractical? Please give a quantitative answer. Hint: Humid air has a dielectric (breakdown) strength of × 3.0 × 10€ N/C. (c) What is the change AU in the electric potential energy of a released electron when the electric force causes it to move vertically upward through a distance d 520 m? (d) Through what potential change does the electron move?