Electric charge can accumulate on an airplane in flight. You may have observed needle-shaped metal extensions on the wing tips and tail of an airplane. Their purpose is to allow charge to leak off before much of it accumulates. The electric field around the needle is much larger than the field around the body of the airplane, and can become large enough to produce dielectric breakdown of the air, discharging the airplane. To model this process, assume that two charged spherical conductors are connected by a long conducting wire, and a charge of 1.20 +C is placed on the combination. One sphere, representing the body of the airplane, has a radius of 6.00 cm, and the other, representing the tip of the needle, has a radius of 2.00 cm. (a) What is the electric potential of each sphere? (b) What is the electric field at the surface of each sphere?

You and your colleagues have been tasked with launching a weather balloon into the Earth's stratosphere via rocket ship. In order to reduce fuel usage to meet with newly imposed fuel-consumption regulations, you are hoping to use the electric interaction between charges to your advantage. You have decided on the design below. You are able to place two Q = 1.98 C charges in the rocket ship and into the launching platform so that they are separated by a distance of yo = 2.93 m. You are allowed enough fuel to boost the rocket to an initial speed of vo = 309 m/s without accounting for the extra boost from the charges. The rocket on its own has a mass of 2.095x104 kg. The more equipment you can attach to your weather balloon (which is inside the rocket), the better. What limit do you put on the mass of the weather balloon and attached equipment? You may want to know the formula for gravitational potential energy for an object of mass m and height h: Egray = mgh, where g=9.81 m/s?. Edge of…

A spherical capacitor is composed of two concentric conducting spheres, one of radius a and the other of radius c (c > a). In addition, between the two conductors there is a spherical shell of dielectric material (relative permittivity/relative dielectric constant ) with inner radius b (c > b > a) and outer radius c. The charge on the inner conductor is +Q. The charge on the outer conductor is -Q. (a) Make a sketch of the situation, indicating the relevant dimensions. (b) Determine the magnitude of the electric field E at radius r for a < r < b. (c) Determine the magnitude of the electric field E at radius r for b < r < c. (d) What is the (induced) surface charge density on the inner surface of the dielectric. (e) Sketch the radial component of the electric field versus r . (f) Sketch the electrostatic potential versus r . (g)Calculate the potential difference between the conductor at r = a and that at r = c. (h) What is the capacitance of this capacitor?