(a) Capacitance is given by
C=4*pi*epsilon*radius=5.56*10^(-11) F
(b) if two sphere
let capacitance be C'

if k=1485
capacitance=C'=kC=1.65*10^(-7) F
A conducting sphere has radius R_1 = 0.5m Calculate the capacitance of the sphere with respect...
A dielectric sphere of radius a has a ”frozen in” polarization
given by P (r) = krrˆ in standard spherical coordinates, with the
origin of the coordinate system at the center of the sphere. (A)
The sphere is surrounded by a conducting shell of inner radius a
and outer radius b > a. The total charge on the conducting shell
is zero. Is there an induced charge on the inner and outer surfaces
of the conducting shell? If so, what...
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 sphere with radius ? = 5 ?? has a charge ? = 8 ??. It is placed at the center of a neutral conducting shell with inner radius ? = 10 ?? and outer radius ? = 15 ??, as shown in the diagram at right. 4. Let the electric potential be equal to zero at infinity. What are the electric potentials of the inner sphere and outer shell? 5. Sketch a graph of the electric potential as...
A solid sphere of radius (a = 3.00 cm) is concentric with a spherical conducting shell of inner radius (b = 2.00 cm) and outer radius (c = 2.40 cm) . The space between the sphere and the inner surface of the shell is empty. The sphere, made of a dielectric, has a net uniform charge of (q1 = +5 micro Coulombs). The shell has a net charge (q2 = - q1) . 1) What is the magnitude of the...
A conducting sphere of radius a has a charge of Q_1 and a
non-conducting shell of inner radius b and outer radius c has a
charge of Q_2. The volume charge density of the non-conducting
shell is given by ρ and is given to be constant. Determine the
volume charge density ρ of the non-conducting shell. Determine the
electric field in the four regions. (r < a, a ≤ r ≤
b, b ≤ r ≤ c, and r > c). Show all...
A solid conducting sphere of radius a has a non-uniform volumetric charge density given bye()-r (where k is some constant). Assume the sphere is surrounded by a concentric conducting shell of radius b and that the space between the sphere and the shell is filled with a weakly conducting fluid of conductivity σ 1. Find an expression that represents the resistance between the sphere and the shell assuming they are maintained at a potential difference ΔV. If the fluid is...
A conducting sphere with radius R has total charge Q. (a) Find the relationship between the magnitude of the electric field and the electric potential on the surface of the conducting sphere. (Use the following as necessary R, Q, and E for the magnitude of the electric field.) V = (b) For a sphere of radius 77 cm, calculate the maximum surface electric potential at which the surrounding air begins to break down. Take the dielectric strength of (maximum sustainable...
3. (8 points) Consider a conducting sphere with total electric charge +Q with radius Rị centered at p= 0 (spherical coordinates). The surface charge at r = R1 is spread uniformly on this spherical surface. There is also an outer conducting shell of radius r = R2, centered at r = 0 and with total electric charge - Q also spread uniformly on the surface. This arrangement of separated positive and negative charge forms a capacitor. We will assume that...
A solid conducting sphere of radius 2.00 cm has a charge 10.80 µC. A conducting spherical shell of inner radius 4.00 cm and outer radius 5.00 cm is concentric with the solid sphere and has a charge -2.50 µC. Find the electric field at the folowing radii from the center of this charge configuration. a) r=1.00 cm b)r=3.00 cm c)r=4.50 cm d) r=7.00 cm
A solid conducting sphere of radius 2.00 cm has a charge 10.80 µC. A conducting spherical shell of inner radius 4.00 cm and outer radius 5.00 cm is concentric with the solid sphere and has a charge -2.50 µC. Find the electric field at the folowing radii from the center of this charge configuration. a) r=1.00 cm b)r=3.00 cm c)r=4.50 cm d) r=7.00 cm