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The current density in the long, cylindrical wire shown in the accompanying figure varies with distance r from the center of the wire according to J = cr, where c is a constant. (a) What is the current through the wire? (b) What is the magnetic field produced by this current for r ≤ R? For r ≥ R?
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- Nonuniform displacement-current density. The figure shows a circular region of radius R = 5.0 cm in which a displacement current is directed out of the page. The magnitude of the density of this displacement current is given by Jo (9 A/m2)(1-r/R), where r is the radial distance (r< R). What is the magnitude of the magnetic field due to the displacement current at (a) r = 2.5 cm and (b) r= 6.5 cm? RA long, cylindrical conductor of radius R carries a current I as shown in the figure below. The current density J, however, is not uniform over the cross-section of the conductor but is a function of the radius according to J = 2br, where b is a constant? Find an expression for the magnetic field magnitude B at the following distances, measured from the axis. (Use the following variables as necessary: ?0, r1, r2, b, R.) (a) r1 < R (b) r2 > RA particle having mass m = 2.80E-4 kg carries a negative charge q= −1.70E-6 C . The particle is given an initial velocity in the −y direction (downward), as shown in the figure, of v = 3.65E2 m/s. Everywhere in space there is a uniform constant magnetic field B = 0.340 T pointing in the +z direction, which is out of the plane of the page. What is the radius of the cyclotron orbit trajectory that this particle will move along (in m)?
- Suppose that the current density carried by an infinite cylindrical wire is not uniform but in fact varies as Jz(u) = J0 * [1 - (u2 / R2)], where J0 is the value of the current density at the wire's center, R is the radius of the wire, and u is distance from the axis of the wire. Assuming that the magnetic field is circular, compute the wire's magnetic field both inside and outside the wire. (Ampere's law makes even nonuniform current densities manageable.) (Hint: The answer is BФ = 0.25 * μ0 * J0 * R on surface at u = R.)A conducting plate of thickness d carrying the current density of the field is placed in a region with an external magnetic field. Due to the influence of this conductor, the magnetic field in the chamber becomes separated by a magnitude of B₁ on the left side of the plate and B₂ on the other side. Determine the magnitude and direction of the plane current density carried by the plate for the two cases in the figure!A particle having mass m = 2.80E-4 kg carries a negative charge q= −1.70E-6 C . The particle is given an initial velocity in the −y direction (downward), as shown in the figure, of v = 3.65E2 m/s. Everywhere in space there is a uniform constant magnetic field B = 0.340 T pointing in the +z direction, which is out of the plane of the page. What is the radius of the cyclotron orbit trajectory that this particle will move along (in m)?
- Two long wires a positioned as shown below -- one along the x direction and one along y direction. Each wire has a current of 10 A in the indicated directions and the top wire is 10 cm above the bottom wire. What is the angle of the B field exactly half-way between the two wires in degrees? We define to the right as 0 degrees, up as 90, left as 180, and down as 270. What is the magnitude of the magnetic field in μT to 3 significant digits?A particle having mass m = 2.80E-4 kg carries a negative charge q= −1.70E-6 C . The particle is given an initial velocity in the −y direction (downward), as shown in the figure, of v = 2.41E2 m/s. Everywhere in space there is a uniform constant magnetic field B = 0.340 T pointing in the +z direction, which is out of the plane of the page. What is the the magnetic force that B exerts on the particle (in N; use positive sign if the force points in the +x direction and negative sign if the force points in the −x direction)?