An electric current is flowing through a long cylindrical conductor with radius a = 0.75 m. The current density J = 9.5 A/m2 is uniform in the cylinder. In this problem we consider an imaginary cylinder with radius r around the axis AB. 1. For r = 0.5 a, calculate the numerical value of B in Tesla.  2. Express the magnitude of the magnetic field, B, at r > a in terms of I and r.  3. Express B in terms of J, a and r.  4. For r = 2 a, calculate the numerical v

A 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 > R

An infinitely long, straight, cylindrical wire of radius R has a uniform current density J = Jî in cylindrical coordinates. What is the magnitude of the magnetic field at some point inside the wire at a distance r; < R from the wire's central Cross-sectional view axis? Express your answer in terms of R, r;, µo, and J. J B = Side view Assuming J is positive, what is the direction of the magnetic field at some point inside the wire? O positive z-direction negative z-direction positive r-direction negative r-direction positive p-direction negative p-direction

A circular closed, conducting loop of radius r is in the presence of a uniform magnetic field that points into the page, shown in the figure below. The strength of the magnetic field changes as a function of time, which is described by the following expression: B(t) = B1t? + Bo. You may assume that B1 and Bo are both positive numbers. The direction of the magnetic field stays constant. The total resistance of the conducting loop is R. Use this information to solve parts (a) - (d). Write your answers in terms of known quantities such as: r, R, B1, Bo, and t. B(t) = B,t? + Bo %3D R r (a) Write an expression for the magnetic flux through the loop, assuming that the area vector of the loop points out of the page. Is the flux increasing or decreasing over time? (b) Determine the magnitude of the induced electromotive force driven through the loop. (c) Determine the magnitude of the induced current driven through the loop. (d) In which direction does the induced current flow (clockwise or…