Problem 3: An infinitely long solid cylinder of radius 2 m along the z-axis carries a...
Problem 4, 30 marks The infinitely long conducting cylinder of radius R carries the volume current density directed along its axis whose absolute value is a cubic function of the distance from the center of the cylinder r, j(r)-br3, where b is a known constant. a. Find the magnitude and direction of the magnetic field B forr>R. b. Find the magnitude and direction of the magnetic field B for r<R. c. Imagine that the conductor has magnetic permeability H (5...
5. An infinitely long cylinder of radius R carries a frozen-in" magietization parallel to z-axis and is given by M = ksi, where k is a constant and s is the distance from the axis. There is no free current anywhere. Find the magnetic field inside and outside the cylinder.
An infinitely long cylinder with axis aloong the z-direction and radius R has a hole of radius a bored parallel to and centered a distance b from the cylinder axis (a+b<R). The charge density is uniform and total charge/length is placed on the cylinder. Find the magnitude and direction of the electric field in the hole.
An infinite solid cylinder conductor of radius a = 3cm centered on the z-axis carries a current I1 = 1A. The current is evenly distributed along the cross section and is directed out of the screen (positive z-axis direction). An infinite coaxial conductive surface of radius b = 8 cm carries a current I2 = 4A, towards the inside of the screen (negative direction z). What is the magnitude of the magnetic field B inside the inner cylinder at a...
An infinitely long solid insulating cylinder of radius a = 5.5 cm is positioned with its symmetry axis along the z-axis as shown. The cylinder is uniformly charged with a charge density rho = 25 mu C/m^3. Concentric with the cylinder is a cylindrical conducting shell of inner radius b = 14.4 cm, and outer radius c = 17.4 cm. The conducting shell has a linear charge density lambda = -0.42 mu C/m. 1) What is E_y(R), the y-component of...
Electrostatics problem 2. An infinitely long circular cylinder of radius a and dielectric constant E is placed with its axis along the z-axis and is put in an electric field which would have been uniform in the absence of the cylinder, pointing along the x-axis (see figure). Find the total electric field at all points outside and inside the cylinder. Find the bound surface charge density.
Consider two concentric, infinitely long cylinders. The cylinders are oriented such that the center-line is along the z-axis, and the radii exist in the r-direction. The inner cylinder has a radius of ra and the outer cylinder has a radius rb. The inner cylinder moves in the positive z-direction with a velocity W while the outer cylinder is held stationary. The fluid contained between the cylinders is assumed to be Netwonian, incompressible, isotropic and isothermal. The flow of the fluid...
A long, straight, solid cylinder, oriented with its axis in the z−direction, carries a current whose current density is J⃗ . The current density, although symmetrical about the cylinder axis, is not constant but varies according to the relationship J⃗ =2I0πa2[1−(ra)2]k^forr≤a=0forr≥a where a is the radius of the cylinder, r is the radial distance from the cylinder axis, and I0 is a constant having units of amperes. A)Using Ampere's law, derive an expression for the magnitude of the magnetic field...
Consider two concentric, infinitely long cylinders. The cylinders are oriented such that the center-line is along the z-axis, and the radii exist in the r-direction. The inner cylinder has a radius of ra and the outer cylinder has a radius Tb. The inner cylinder rotates with an angular velocity of w whereas the outer cylinder is stationary. There is no pressure gradient applied nor gravity. The fluid contained between the cylinders is assumed to be Netwonian, incompressible, isotropic and isothermal....
A 1.50 m long straight wire lies along the z axis and carries a steady current in the +z direction. A uniform magnetic field exists everywhere in space and is given by B⃗→ = (3.00 i^ + 4.00 j^) T. If the field exerts a force on the wire of magnitude 60.0 N, find the current carried by the wire.