An electrical current with volume current density / passes through a certain region of space producing a magnetic field given by B = 6y2i + x²j. At what point (x, y) of the following points = 0? %3D
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- The vector potential in free space is given as A⃗ =z^20ρ2z. In that case a) Which of the following is the correct magnetic flux density B⃗? b) Which of the following is the correct current density J⃗?An electron with kinetic energy 2.5 keV moving along the positive direction of an x axis enters a region in which a uniform electric field of magnitude 10 kV/m is in the negative direction of the y axis. A uniform magnetic field is to be set up to keep the electron moving along the x axis, and the direction of is to be chosen to minimize the required magnitude of . In unit-vector notation, what should be set up?An ideal toroidal solenoid has an inner radius of 14.5 cm and outer radius of19.0 cm. It carries a current of 0.500 A and has 9500 number of turns. Find themagnetic field strengths at distances 15.0 cm and 20.0 cm from the center of the solenoid.
- A certain commercial mass spectrometer is used to separate uranium ions of mass 3.92 × 10-25 kg and charge 3.20 × 10-19 C from related species. The ions are accelerated through a potential difference of 107 kV and then pass into a uniform magnetic field, where they are bent in a path of radius 0.961 m. After traveling through 180° and passing through a slit of width 0.766 mm and height 1.48 cm, they are collected in a cup. (a) What is the magnitude of the (perpendicular) magnetic field in the separator? If the machine is used to separate out 0.795 mg of material per hour, calculate (b) the current of the desired ions in the machine and (c) the thermal energy produced in the cup in 1.07 h.A parallel-plate capacitor with circular plates of radius R = 16 mm and gap width d = 5.0 mm has a uniform electric field between the plates. Starting at time t = 0, the potential difference between the two plates is V ohm (100 V)e=t/t, where the time constant t = 12 ms. At radial distance r = 0.80R from the central axis, what is the magnetic field magnitude (a) as a function of time for t >- 0 and (b) at time t = 3t?An alpha particle with velocity v = (3 x 105,0,0) m/s enters a region where themagnetic field has a value B = (0,0,1.2) T. Determine the required magnitude and directionof an electric field E that will allow the alpha particle to continue to move along the x axis.
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