Tutorial Exercise An air-filled spherical capacitor is constructed with an inner-shell radius of 6.95 cm and an outer-shell radius of 14.5 cm. (a) Calculate the capacitance of the device. (b) What potential difference between the spheres results in a 4.00-μC charge on the capacitor? Part 1 of 4 - Conceptualize Since the separation between the inner and outer shells is much larger than a typical electronic capacitor with separation on the order of 0.1 mm and capacitance in the microfarad range, we expect the capacitance of this spherical configuration to be on the order of picofarads. The potential difference should be sufficiently low to avoid sparking through the air that separates the shells. Part 2 of 4 - Categorize We will calculate the capacitance from the equation for a spherical shell capacitor. We will then calculate the voltage found from Q = CAV. Part 3 of 4 - Analyze (a) For a spherical capacitor with inner radius a and outer radius b, we have the following for the capacitance. ab C = k₂(b-a) 0.0695 0.0695 m 0.145 0.145 m . (8.99 x 109 N m²/c²) 0.145 0.145 m 0.0695 1.484 1.48 x 10 11 F = 14.84 14.8 PF Part 4 of 4 - Analyze (b) The change in voltage across a capacitor of charge Q is given by AV = 5 × 0.0695 m Your response differs from the correct answer by more than 10%. Double check your calculations. x 1.484 × 10-11 F) Your response differs from the correct answer by more than 10%. Double check your calculations. KV. 10-6 c) = = 337

In a certain region of space, the electric field is zero. From this fact, what can you conclude about the electric potential in this region? (a) It is zero, (b) It does not vary with position. (c) It is positive. (d) It is negative. (e) None of those answers is necessarily true.

A 6.50-F capacitor is connected to a battery. What is the charge on each plate of the capacitor if the voltage of the battery is a. 10.0 V and b. 2.00 V?

Why do we need to be careful about work done on the system versus work done by the system in calculations?

In different experimental trials, an electron, a proton, or a doubly charged oxygen atom (O--), is fired within a vacuum tube. The particle's trajectory carries it through a point where the electric potential is 40.0 V and then through a point at a different potential. Rank each of the following cases according to the change in kinetic energy of the particle over this part of its flight from the largest increase to the largest decrease in kinetic energy. In your ranking, display any cases of equality, (a) An electron moves from 40.0 V to 60.0 V. (b) An electron moves front 40.0 V to 20.0 V. (c) A proton moves from 40.0 V to 20.0 V'. (d) A proton moves from 40.0 V to 10.0 V. (e) An O-- ion mines from 40.0 V to 60.0 V.

When a 360-nF air capacitor is connected to a power supply, the energy stored in the capacitor is 18.5J . While the capacitor is connected to the power supply, a slab of dielectric is insetted that completely fills die space between the plates. This increases the stored energy by 23.2J . (a) What is the potential difference between the capacitor plates? (b) What is die dielectric constant of the slab?

An electrostatic paint sprayer has a 0.200-m-diameter metal sphere at a potential of 25.0 kV that repels paint droplets onto a grounded object. (a) What charge is on the sphere? (b) What charge must a 0.100-mg drop of paint have to arrive at the object with a speed of 10.0 m/s?

A particle of mass m and charge q moves along a straight line away from a fixed particle of charge Q. When the distance between the two particles is r0 , q is moving with a speed v0 . (a) Use the work-energy theorem to calculate the maximum separation of the charges. (b) What do you have to assume about v0 to make this calculation? (c) What is the minimum value of v0 such that q escapes from Q?

The surface charge density on a long straight metallic pipe is . What is the electric potential outside and inside the pipe? Assume the pipe has a diameter of 2a.

A research Vail de Graaff generator has a 2.00-m- diameter metal sphere with a charge of 5.00 mC on it. (a) What is the potential near its surface? (b) At what distance from its center is the potential 1.00 MV? (c) An oxygen atom with three missing electrons is released near the Van de Graaff generator. What is its energy in MeV when the atom is at the distance found in part b?