2. A cylindrical bar magnet has magnetization M(r), a general function of r directed (a) axially,...
2. A cylindrical bar magnet has magnetization M(r), a general function of r directed (a) axially, (b) azimuthally or (c) radially (here with M(0)- 0). In each case find Br). In (a) also find the magnetization current encircled by a rectangle of axial length i, extending from radial distance r inside the cylinder to the outsidemrim ma wontoor dall % in (b) find the current encircled by a circle of radius r.
2. A cylindrical bar magnet has magnetization M(r),...
3. A cylindrical bar magnet has radius a and finite length 2, centered at the origin; it has uniform axial magnetization M. (a) Detail the correspondence with the solenoid in HW 5, #3: Evaluate the magnetzation surface-current density i and check the value found for the total magnetic dipole moment m against the definition of M as its volume-density. (b) Express B(o and H) on the axis, inside and outside the magnet, in terms of M, I , a, and乙Draw...
A uniform electric field is directed axially in a cylindrical region that includes a rectangular loop of wire with total resistance RR. This loop has radially oriented width aa and axially oriented length bb, and sits tight against the cylinder axis, as shown in (Figure 1). The electric field is zero at time tt = 0 and then increases in time according to E⃗ =ηt2k^E→=ηt2k^, where ηη is a constant with units of V/(m⋅s2)V/(m⋅s2).
(2) 4.[4pts) An infinitely long cylinder of radius R carries NO free current but magnetization M=ks, where k > 0 is a constant and s is the cylindrical radius from the axis. Find the magnetic field B due to M both inside and outside of the cylinder.
#6) (25 pts total) An infinitely long cylinder of radius R carries a “frozen-in” magnetization parallel to the axis M = kpa, where k is a constant and pis the distance from the axis. (a) (12 pts) Calculate all the bound currents. (b) (13 pts) Find the magnetic field, B, inside and outside of the cylinder. (This is for cylindrical coordinates where "s" is the same as “p”)
The current density inside a long, solid, cylindrical wire of
radius a = 4.0 mm is in the direction of the central axis
and its magnitude varies linearly with radial distance r
from the axis according to J =
J0r/a, where
J0 = 280 A/m2. Find the magnitude of
the magnetic field at a distance (a) r=0, (b) r = 2.7 mm
and (c) r=4.0 mm from the center.
Chapter 29, Problem 047 The current density inside a long, solid,...
A long, cylindrical wire of radius R has a current density J(r) = Jo(1 – r2/R2) for distances where r < R and J(r) = 0 for r < R where r is the distance from the center of the wire’s axis. Find the magnetic field strength inside (r < R) and outside (r > R) the wire. Sketch the magnetic field strength as a function of distance r from r = 0 to r = 2R. Find the location...
(1 point) [DL:2/5] A cylindrical conductor of radius R = 0.85 m is centred on the z-axis. The current density in the conductor is given in cylindrical coordinates: J = 16e (1-p/R)a, A/m? 'a, A/m² Find the total current passing through the plane z = 0. 146.8/e
An infinitely long cylinderical capacitor initially has a linear charge density of + 5.60 nC/m (nanocoloumbs per meter) on the inner conducting cylinder and -5.60 nC/m on the outer conducting cylinder. The radius of the inner conducting cylinder is a = 0.060 m and the radius of the outer conducting shell is b = 0.160 m. See the figure of a small piece of the capacitor below: Part A Find the magnitude of the electric field 0.019 m from the...
L(a) A long (L>> a) cylinder in vacuum has a line charge density p is shown below, (). State the Gauss's law for electric field in words. [1) (i). In order to calculate the electric field inside the cylinder using Gauss's Law, draw an appropriate Gaussian surface in the cylinder. [1] (i). Use the above information or otherwise, show that the electric field in the radial direction Pt inside the cylinder is ,2a (assume that the charge is evenly distributed...