1. Consider the uniformly magnetized infinite circular cylinder of radius R at z-axis. The magnetization inside the cylinder is M = M₁2. (a) Find the H everywhere in space (b) Find the B everywhere in space
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- A cyclotron (figure) designed to accelerate protons has an outer radius of 0.333 m. The protons are emitted nearly at rest from a source at the center and are accelerated through 572 V each time they cross the gap between the dees. The dees are between the poles of an electromagnet where the field is 0.720 T. The black, dashed, curved lines Alternating AV represent the path of the particles. -Dg After being accelerated, the particles exit here. -North pole of magnet (a) Find the cyclotron frequency for the protons in this cyclotron. 1.04e33 x rad/s (b) Find the speed at which protons exit the cyclotron. m/s (c) Find their maximum kinetic energy. ev (d) How many revolutions does a proton make in the cyclotron? revolutions (e) For what time interval does the proton accelerate? awranca Barke kay Nationallab3. You are conducting a magnetic survey in Minnesota with a proton-precession magnetometer with a sensitivity of 1 nT. Make some simplifying assumptions (e.g. I=90°) and estimate how far away from the magnetic senor you need to be from a 2000-pound (=1 ton) car (on the surface) so that the magnetic signal is less than 1 nT? The magnetic moment for typical iron and steel objects is 100 Am/ton.A solid cylinder has a uniform magnetization M throughout the volume in the z direction Where are the bound currents? Select one: O a side rounded surface only O b. every where in the volume and surface O C. top, bottom surface only O d. Volume only not surface O e. All surfaces but not volume
- Can you distinguish between Gauss law in electrostatics and magnetism?Specifically, explain the reason, why divergence of magnetic field is zero?5. If the magnetic vector potential in a region is given as A = K{x(x²+y°)+ÿ(z+r)+2ry), where K is some constant, determine the magnetic field H in a vacuum medium.A small rod magnet has a magnetic field at a distance from it as large as Hom B = 2nz3 Where z is the distance from the magnet on the axis connecting the north pole and south, m is the moment of magnetic dipole. Assuming electrons orbit protons like small rod magnets, determine the m magnetic dipole of an electron orbiting an atom.
- 31. Consider the four point charges arranged on the corners of a square as shown. Let the direction up towards the top of the page be N. The electric field at the center of the square will point (a) N (b) S (c) E (d) W (e) NE (d) NW (e) SE (f) SW +4 d 2. The diagram shows a current loop carrying current as shown. It is effectively (a) a north pole of a magnet (b) a south pole of a magnet (c) a monopole (d) not a magnet at all3. A long cylindrical wire of radius R carrios a current I. The current density is non-uniform and can be expressed as J(r) = Jor? for 0 < rA wire with a constant linear charge density of 4.0 C/m is located at the origin and oriented along the y-axis. A -3.0 C charge is placed along the x-axis at position x=-0.50 m. Find the electric force on the -3.0 charge.Please provide correct answers. Use the following constants if necessary. Coulomb constant, k = 8.987×10^9 N⋅m^2/C^2 . Vacuum permitivity, ϵ0= 8.854×10^−12 F/m. Magnetic Permeability of vacuum, μ0 = 12.566370614356×10^−7 H/m. Magnitude of the Charge of one electron, e = −1.60217662×10^−19 C. Mass of one electron, m_e = 9.10938356×10^−31 kg. Unless specified otherwise, each symbol carries their usual meaning. For example, μC means microcoulomb .5. A cylindrical conductor with radius R carries a current that is nonuniformly distributed over the cross-section of the conductor, whose the current density is J = ar, a is a constant and > is the radial distance from the cylinder axis. (1) Find the total current in the conductor. (2) Find the magnetic field B as a function of the distance from the conductor axis for points both inside (r R) the conductor.