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.

Expert Solution

genius_generous answered 1 year ago

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 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.

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

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, 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 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 uniform solid sphere with Radius R has KE (rotational) at an angular speed of w...

A uniform solid sphere with Radius R has KE (rotational) at an angular speed of w when spinning about an axis through its center. A uniform thin-walled hollow shell of radius 2R has 1/3 KE (rotational) at an angular speed of w when spinning about an axis through its center. If m=M for solid sphere, whats the mass of the hollow sphere?

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.

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 very long solid conducting cylinder of length L and radius R carries a uniform surface...

A very long solid conducting cylinder of length L and radius R carries a uniform surface current over the whole outer surface of the cylinder. The surface current is along Z and parallel to the XY-Plane. Use the Biot-Savart law to calculate the B field inside, at the middle of the cylinder. Thanks!

Question