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Using integrals, calculate the volume of the smaller of the two portions in which a sphere...
Tangent plane to a sphere: Consider the sphere of radius R centered on the origin in...
Tangent plane to a sphere: Consider the sphere of radius R centered on the origin in 3 dimensions. Now consider the point o = Doi+yoj + zok. Write the equations for any two (non-parallel) planes which pass through both the point to and the origin. Using these planes, write the equation for the tangent plane of the sphere at the point to. (Hint: think about how the tangent plane of a sphere must be perpendicular to a line connecting the...
A sphere of radius R and surface charge density η is positioned with its center a...
A sphere of radius R and surface charge density η is positioned with its center a distance 2R above a horizontal infinite plane with the same surface charge density η. Write the electric field on the line perpendicular to the plane and passing through the center of the sphere (in between the plane and the surface of the sphere)
Use rectangular, cylindrical and spherical coordinates to set up the triple integrals representing the volume of the region bounded below by the xy plane, bounded above by the sphere with radius and...
Use rectangular, cylindrical and spherical coordinates to set up the triple integrals representing the volume of the region bounded below by the xy plane, bounded above by the sphere with radius and centered at the origin the equation of the sphere is x2 + y2 + z2-R2), and outside the cylinder with the equation (x - 1)2 +y2-1 (5 pts each) Find the volume by solving one of the triple integrals from above.( 5 pts) Total of 20 pts)
Use...
using Java The formula to compute the volume of a sphere is: volume = ( 4...
using Java The formula to compute the volume of a sphere is: volume = ( 4 3 ) π r 3 where r is the radius of the sphere and π is 3.14159. Assume a variable radius has already been declared (type double) and initialized with the value of the radius of a sphere. Write java statements to do the following: Declare a constant PI and initialize it to 3.14159 Declare a variable volume of type double Calculate the volume...
Charge Q is distributed uniformly throughout the volume of an insulating sphere of radius R =...
Charge Q is distributed uniformly throughout the volume of an insulating sphere of radius R = 4.00 cm. At a distance of r = 8.00 cm from the center of the sphere, the electric field due to the charge distribution has magnitude 640 N/C . a. What is the volume charge density for the sphere? Express your answer to two significant figures and include the appropriate units. b. What is the magnitude of the electric field at a distance...
Consider a sphere of radius a with a uniform charge distribution over its volume, and a...
Consider a sphere of radius a with a uniform charge distribution over its volume, and a total charge of q_o. Use Gauss's Law to calculate the electric field outside the sphere, and then inside the sphere. Solve the general problem in r, recognizing that problem spherical symmetry. Draw a graph of the electric field the has the surface of the strength as a function of noting where if the surface of the sphere is (a). Some hints: the surface area...
possible. 1. A sphere of radius R consists of linear material of dielectric constant x. Embedded...
possible. 1. A sphere of radius R consists of linear material of dielectric constant x. Embedded in the sphere is a free-charge density ρ= k/r, where k is constant and r is the distance from the sphere's center. (a) Show that ker 2REo is the electrie field inside the sphere. (b) The electric field outside the sphere is 26or2 Find the scalar potential at the center of the sphere, taking the zero of potential at infinite radial distance 2. In...
A solid sphere of nonconducting material has a uniform positive charge density ρ (i.e. positive charge...
A solid sphere of nonconducting material has a uniform positive charge density ρ (i.e. positive charge is spread evenly throughout the volume of the sphere; ρ=Q/Volume). A spherical region in the center of the solid sphere is hollowed out and a smaller hollow sphere with a total positive charge Q (located on its surface) is inserted. The radius of the small hollow sphere R1, the inner radius of the solid sphere is R2, and the outer radius of the solid...
A sphere of radius a is made of a nonconducting material that has a uniform volume charge density p.
A sphere of radius a is made of a nonconducting material that has a uniform volume charge density p. A spherical cavity of radius b is removed from sphere which is a distance z from the center of the sphere. Assume that a > z + b. a) Find the magnitude and direction of the electric field at point y0 which is separated by distance yo from the center of the sphere. b) Find the magnitude and direction of the electric field...
A nonconducting sphere of radius r0 carries a total charge Q distributed uniformly throughout its volume....
A nonconducting sphere of radius r0 carries a total charge Q distributed uniformly throughout its volume. Part A: Determine the electric potential as a function of the distance r from the center of the sphere for r>r0. Take V=0 at r=?. Part B: Determine the electric potential as a function of the distance r from the center of the sphere for r<r0. Take V=0 at r=?. Express your answer in terms of some or all of the variables r0, Q,...
Tangent plane to a sphere: Consider the sphere of radius R centered on the origin in 3 dimensions. Now consider the point o = Doi+yoj + zok. Write the equations for any two (non-parallel) planes which pass through both the point to and the origin. Using these planes, write the equation for the tangent plane of the sphere at the point to. (Hint: think about how the tangent plane of a sphere must be perpendicular to a line connecting the...
Use rectangular, cylindrical and spherical coordinates to set up the triple integrals representing the volume of the region bounded below by the xy plane, bounded above by the sphere with radius and centered at the origin the equation of the sphere is x2 + y2 + z2-R2), and outside the cylinder with the equation (x - 1)2 +y2-1 (5 pts each) Find the volume by solving one of the triple integrals from above.( 5 pts) Total of 20 pts)
Use...
Consider a sphere of radius a with a uniform charge distribution over its volume, and a total charge of q_o. Use Gauss's Law to calculate the electric field outside the sphere, and then inside the sphere. Solve the general problem in r, recognizing that problem spherical symmetry. Draw a graph of the electric field the has the surface of the strength as a function of noting where if the surface of the sphere is (a). Some hints: the surface area...
possible. 1. A sphere of radius R consists of linear material of dielectric constant x. Embedded in the sphere is a free-charge density ρ= k/r, where k is constant and r is the distance from the sphere's center. (a) Show that ker 2REo is the electrie field inside the sphere. (b) The electric field outside the sphere is 26or2 Find the scalar potential at the center of the sphere, taking the zero of potential at infinite radial distance 2. In...
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