A rectangular wire loop located in the plane of the page has a width L, and its length, x, is determined by the position a movable rail that forms the fourth side of the rectangle, as shown. The total electrical resistance of the wire loop is R, and an externally applied magnetic field, B, is directed out of the page. The rail is moving towards the right with speed v. Assume that the x direction is towards the right of the page, the y direction is towards the top of the page, and the z direction is out of the page. |M|= Using only the variables provided, what is the magnitude of the magnetic flux at the instant when the rectangle has length x? Using only the variables provided, what is the magnitude of the induced EMF in the loop? What is the direction of the EMF generated in the loop? What is the magnitude of the induced current in the loop? What external force, Fapplied, must be applied to the rail to keep it moving to the right at constant speed v? Give both the magnitude and direction Based upon the calculation of the force, Fapplied, calculated in the previous step, how much power must be put into the system in order to maintain of the rail? Considering the current calculated in a previous step, calculate the power dissipated through the resistor. Which statement best describes the flow of energy through the system?

Is B constant in magnitude for points that lie on a magnetic field line?

A long, solid, cylindrical conductor of radius 3.0 cm carries a current of 50 A distributed uniformly over its cross-section. Plot the magnetic field as a function of the radial distance r from the center of the conductor.

Two long coaxial copper tubes, each of length L, are connected to a battery of voltage V. The inner tube has inner radius o and outer radius b, and the outer tube has inner radius c and outer radius d. The tubes are then disconnected from the battery and rotated in the same direction at angular speed of radians per second about their common axis. Find the magnetic field (a) at a point inside the space enclosed by the inner tube r d. (Hint: Hunk of copper tubes as a capacitor and find the charge density based on the voltage applied, Q=VC, C=20LIn(c/b) .)