Given a magnetic vector potential A = 3ρe-z aφ, what is the magnetic flux through the surface z = -5, 0 < ρ < 3?
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Given a magnetic vector potential A = 3ρe-z aφ, what is the magnetic flux through the surface z = -5, 0 < ρ < 3?
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- Is the following True or False for the Gauss's Law for magnetic field? Since there are no magnetic monopoles, magnetic field lines can not start or end anywhere. They always come as loops. That is why magnetic flux through a closed surface is always zero: OB dA = 0 O True O FalseA positively charged particle slides off a frictionless and smooth surface with initial X X X X X X X X speed v, =v, . It then enters into a region with X X X X X x x x X uniform magnetic field pointing into the page. X X X X x x x x X x x x x x X x x x The particle eventually hits the ground with final speed v, air time and range S · The particle slides off the edge again with identical initial speed, but this time without the magnetic field. The particle then hits the ground with final speed v,, air time t, , and range s,. Determine the relationships between v, and v,, t, and t, , as well as s, and s, (3 marks). Please note that no calculation is needed. You were to provide the relationship in the sense that whether one variable is greater than, smaller than, or equals to the other one (>, <, or =). Provide a rough explanation (3 marks).Figure (a) shows a wire that forms a rectangle (W = 19.0 cm, H = 29.0 cm) and has a resistance of 4.50 mQ. Its interior is split into three equal areas, with magnetic fields B and B B 2' The fields are uniform within each region and directly out of or into the page 1, 3. as indicated. Figure (b) gives the change in the z components B, of the three fields with time t; the vertical axis scale is set by Bg = 4.50 µT and Bp = -2.50B5. What are the (a) the magnitude and (b) direction of the current induced in the wire? B5 H B2 t (s) (a) (b) (a) Number i 2.75E-5 Units A (h) COunterclockwise B. (uT)
- In the figure, an electron accelerated from rest through potential difference V1-1.26 kV enters the gap between two parallel plates having separation d = 19.6 mm and potential difference V2- 52.4 V. The lower plate is at the lower potential. Neglect fringing and assume that the electron's velocity vector is perpendicular to the electric field vector between the plates. In unit-vector notation, what uniform magnetic field allows the electron to travel in a straight line in the gap? Number ( o ĵ+ i R) Units mT 124.7A magnetic dipole moment of m = (7.50, -8.38, 4.59) Am² is inside a uniform magnetic field of B = (3.34, -6.77, 6.79) T. What is the potential energy of the dipole? (a) What is the angle between the magnetic dipole moment vector and the magnetic field vector? (b) What is the magnitude of the torque acting on the dipole?An infinite rectangular slab of thickness 2d is situated parallel to the x-y plane, with its center at z = 0. Its upper surface is situated at z = d, and its lower surface is at z = -d. The material is uniformly magnetized given by M = Moi, and there are no free currents everywhere. Solve for the magnetic field outside and inside the slab. Verify this by relating it to the auxiliary field given by Ā 1B-M. μο Hint: There is no magnetization outside the slab.
- A metal cylinder with a radius "R" is placed with its central axis aligned with the z axis. A current, I, flows along its surface only (no current flows on the interior of the cylinder). Calculate the magnetic field strength as a function of distance, r, away from the center of the cylinder for two different regions: (a) r<R and (b) r>R.A student makes a short electromagnet by winding 530 turns of wire around a wooden cylinder of diameter d = 4.4 cm. The coil is connected to a battery producing a current of 4.1 A in the wire. (a) What is the magnitude of the magnetic dipole moment of this device? (b) At what axial distance z >> d will the magnetic field have the magnitude 6.7 µT (approximately one-tenth that of Earth's magnetic field)?In the figure, an electron accelerated from rest through potential difference V₁-1.03 kV enters the gap between two parallel plates having separation d-17.2 mm and potential difference V₂-108 V. The lower plate is at the lower potential. Neglect fringing and assume that the electron's velocity vector is perpendicular to the electric field vector between the plates. In unit- vector notation, what uniform magnetic field allows the electron to travel in a straight line in the gap? Number (0 7+0 3.30e-4 A) Units mT
- The magnetic dipole moment of the nickel atom is about 5.6 x 10-24 A· m2. (a) Calculate the maximum magnetic dipole moment (in A •m²) of a domain consisting of 1019 nickel atoms. A: m2 (b) What current (in A) would have to flow through a single circular loop of wire of diameter 2.2 cm to produce the magnetic dipole moment you calculated? AThe magnetic dipole moment of the cobalt atom is about 1.6 x 10-23 A · m². (a) Calculate the maximum magnetic dipole moment (in A •m²) of a domain consisting of 1020 cobalt atoms. A•m2 (b) What current (in A) would have to flow through a single circular loop of wire of diameter 2.6 cm to produce the magnetic dipole moment you calculated? AA cube of edge length e = 6.0 cm is positioned as shown in the figure below. There is a uniform magnetic field throughout the region with components B, = +7.0 T, B, = +2.0 T, and B, = +7.0 T. (a) Calculate the flux through the shaded face of the cube. T•m2 (b) What is the net flux emerging from the volume enclosed by the cube (i.e., the net flux through all six faces)? T•m²