An air-filled spherical capacitor is constructed with an inner-shell radius of 6.50 cm and an outer-shell radius of 12.6 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?
(c) What If? What would be the length (in cm) of a cylindrical air-filled capacitor with the same inner and outer radii as the spherical capacitor if it were to have the same capacitance as the spherical capacitor?
An air-filled spherical capacitor is constructed with an inner-shell radius of 6.50 cm and an outer-shell radius of 12.6 cm
A spherical capacitor has an inner-shell radius of 4.10 cm and an outer-shell radius of 7.70 cm. (The capacitance of a spherical capacitor is C = 4πε0[rinrout/(rout − rin)].) (a) What is the capacitance of this capacitor? F (b) When connected to a battery, the capacitor carries a charge of 7.10 µC. What is the voltage of the battery? V
A capacitor is constructed using concentric conducting spheres. The inner sphere has radius a, the outer sphere (a thin-walled shell) has radius b. 1. Show that the capacitance is ab/k(b − a) when the space between the inner and outer spheres is empty. Start with the result from Gauss’s law for the field outside a uniform spherical charge distribution (derive the potenital difference between the spheres). 2. What is the capacitance if a = 0.1 m and b = 0.103...
A conducting spherical shell of inner radius a= 50.0 cm and outer radius b= 60.0 cm has a net charge Q1= -7.00 μC. A second larger conducting shell of inner radius c= 70.0 cm and outer radius d= 80.0 cm has a net charge of Q2= +3.00 μC, and it is concentric with the first shell as shown in the figure to the left. What is the magnitude and direction of the electric field as a function of distance from...
A nonconducting spherical shell, with an inner radius of 3.2 cm and an outer radius of 8.0 cm, has charge spread nonuniformly through its volume between its inner and outer surfaces. The volume charge density ρ is the charge per unit volume, with the unit coulomb per cubic meter. For this shell ρ = b/r where r is the distance in meters from the center of the shell and b = 2.5 μC/m2. What is the net charge in the...
2. (4 points) A spherical capacitor has outer radius R2 and inner radius R1 and is filled with a dielectric material in which ε--Ceo/r. A positive charge Q is placed in the inner radius and a negative charge-Q is placed on the outer radius. Remember that ε in this problem depends on the radial position r. (a) Calculate D, E and P within the capacitor, as a function of r for R R2 b) Calculate the potential V, from R1...
A capacitor is constructed of two concentric conducting cylindrical shells. The radius of the inner cylindrical shell is 2.37 x10-3 m, and that of the outer shell is 2.47 x 10-3 m. When the cylinders carry equal and opposite charges of magnitude 2.0 x 10-10 C, the electric field between the plates has an average magnitude of 3.8 x 104 V/m and is directed radially outward from the inner shell to the outer shell. Determine (a) the magnitude of the...
A spherical, non-conducting shell of inner radius = 10 cm and outer radius = 15 cm carries a total charge Q = 16.2 μC distributed uniformly throughout the volume of the shell. What is the magnitude of the electric field at a distance r = 11.2 cm from the center of the shell? (ε0 = 8.85 × 10-12 C2/N ∙ m2) (Give your answer to the nearest 0.01 MN/C)
A spherical capacitor has a spherical inner plate with radius a and outer plate with radius b. The charge on the inner plate is +Q and on the outer plate it is -Q. We have filled a cone shaped region of angle θ (0 ≤ θ ≤ π) with a dielectric with constant κ. The dielectric fills the entire volume between the two spheres inside the cone. You may neglect any fringing effects between the dielectric and the vacuum (dielectric...
A spherical capacitor has inner radius a and outer radius b, and is filled with an inhomogeneous dielectric with . Show that the capacitance of the capacitor is by assuming. (a) Q0 at the inner sphere and -Q0 at the outer sphere. (b) V0 at the inner sphere and 0 at the outer sphere.
A capacitor is composed of two cylindrical conducting shells. The inner shell has a radius A, is centered inside the outer shell and has a positive surface charge density +3s. The outer shell has radius B = 3A and negative surface charge density -s. Assume the length of the conductors is ?infinitely? long compared to the radius B so that you can ignore all edge effects. Let r be the vector pointing from the center of the capacitor to any...