A solid is bounded by the sphere centered at the origin of radius 5 and the...

A solid is bounded by the sphere centered at the origin of radius 5 and the infinite cylinder along the z-axis of radius 3.

(a) Write inequalities that describe the solid in Cartesian coordinates.

(b) Write inequalities that describe the solid in cylindrical coordinates.

(c) Why is this solid difficult to describe in spherical coordinates? Which of the variables ρ, θ, φ are difficult to describe? Explain.

Solutions

Expert Solution

Colby Messinger answered 1 year ago

Next > < Previous

Related Solutions

A solid sphere of charge is centered at the origin and has radius R = 10...

A solid sphere of charge is centered at the origin and has radius R = 10 cm. Instead of being uniformly charged, the charge density varies with radial position: ρ(r)=ρ0ar. Take a=5.1 m and ρ0=3.7 C/m3. What is the total charge of the sphere? What is the electric flux through a sherical surface of radius R/2 that is concentric with the charged sphere? What is the flux through a spherical surface of radius 2R that surrounds the charged sphere, but...

A solid sphere, radius R, is centered at the origin. The “northern” hemisphere carries a uniform...

A solid sphere, radius R, is centered at the origin. The “northern” hemisphere carries a uniform charge density ρ0, and the “southern” hemisphere a uniform charge density −ρ0. Find the approximate field E(r,θ) for points far from the sphere (r ≫ R). P.S. Please be as neat as possible.

Let S ∈ R3 be the sphere of radius 1 centered on the origin. a) Prove...

Let S ∈ R3 be the sphere of radius 1 centered on the origin. a) Prove that there is at least one point of S at which the value of the x + y + z is the largest possible. b) Determine the point (s) whose existence was proved in the previous point, as well as the corresponding value of x + y + z.

A solid conducting sphere of radius a has its center at the origin and non uniform...

A solid conducting sphere of radius a has its center at the origin and non uniform magnetization given by: M = (a*z^2+b)zhat Estimate the vector potential and the magnetic field in the region of space outside the sphere. Calculate the amount of energy stored in the magnetic field outside the sphere. Explain how there can be an H-field associated with this sphere when there are no free currents.

A solid sphere of radius R is found at the origin. Point mass particles m have...

A solid sphere of radius R is found at the origin. Point mass particles m have elastic collisions with the sphere. Find a relationship between the (scattering) angle and the impact parameter to calculate the differential (cross-section) and the total differential.

A solid sphere of radius R, a solid cylinder of radius R, and a hollow cylinder...

A solid sphere of radius R, a solid cylinder of radius R, and a hollow cylinder of radius R all have the same mass, and all three are rotating with the same angular velocity. The sphere is rotating around an axis through its center, and each cylinder is rotating around its symmetry axis. Which one has the greatest rotational kinetic energy? both cylinders have the same rotational kinetic energy the solid cylinder the solid sphere they all have the same...

A wheeled cart (frictionless), a solid cylinder of radius r, a solid sphere of radius r,...

A wheeled cart (frictionless), a solid cylinder of radius r, a solid sphere of radius r, and a hollow cylinder of radius r are all allowed to roll down an incline. Derive a general relationship for the linear acceleration of each object depending on the angle of the ramp and the rotational inertia. You may assume that the frictional force is small enough that it is only causing rotation in each case.

gaussian surfaces and flux a neutral conducting sphere is centered at the origin and has an...

gaussian surfaces and flux a neutral conducting sphere is centered at the origin and has an inner radius of a and an outer radius if b. at the center of the cavity is a point charge q. what is the formula for the electric field in the folkiwing three regions? o<r<a a<_r<_b b<r repeat provlem assuming that the shell has a net charge of -q.

A hemisphere of radius R is centered on the origin and immersed in an electric field,...

A hemisphere of radius R is centered on the origin and immersed in an electric field, E, given by E = (B cos(θ) / r) r + Ar^2 sin^2 (θ) θ + Cr^3 cos^2 (θ) φ. Find the charge enclosed in the hemisphere

Acircular ring of radius ?lies in the ??plane and is centered on the origin. The half...

Acircular ring of radius ?lies in the ??plane and is centered on the origin. The half on the positive ?side is uniformly charged with a charge +?while the half on the negative ?side is uniformly charged with a total charge −?. a..Draw a diagram of the charge distribution and without doing any math, determinethe direction of the total electric field at the origin . b.Calculate the ?component of the electric field at the origin by integrating the charged ring. i.Draw...

Subjects