The figure below shows two circular regions R1 and R2 with radii r₁ = 22.9 cm and r2 = 31.4 cm. In R₁ there is a uniform magnetic field of magnitude B₁ = 50.6 mT directed into the page, and in R₂ there is a uniform magnetic field of magnitude B₂ = 75.6 mT directed out of the page (ignore fringing). Both fields are decreasing at the rate of 9.80 m/s. Calculate É ds for (a) path 1, (b) path 2, and (c) = f 1 path 3. -Path 3 Path 1 Path 2

Calculate the magnitude of the magnetic field at a point 25.0 cm from a long, thin conductor carrying a current of 2.00 A.

Sketch a plot of the magnitude of the magnetic field as a function of position r for a coax (Fig. P31.27).

A horizontal power line oflength 58.0 in carries a current of 2.20 kA northward as shown in Figure P29.41. The Earths magnetic field at this location has a magnitude of 5.00 10-5 T. The field at this location is directed toward the north at an angle 65.0 below the power line. Find (a) the magnitude and (b) the direction of the magnetic force on the power line.

Acircularcoiofwireofradius5.Ocmhas2Otums and carries a current of 2.0 A. The coil lies in a magnetic field of magnitude 0.50 T that is directed parallel to the plane of the coil. (a) What is the magnetic dipole moment of the coil? (b) What is the torque on the coil?

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.

When the current through a circular loop is 6.0 A, the magnetic field at its center is 2.0104 T. What is the radius of the loop?

Two frictionless conducting rails separated by l = 55.0 cm are connected through a 2.00- resistor, and the circuit is completed by a bar that is free to slide on the rails (Fig. P32.71). A uniform magnetic field of 5.00 T directed out of the page permeates the region, a. What is the magnitude of the force Fp that must be applied so that the bar moves with a constant speed of 1.25 m/s to the right? b. What is the rate at which energy is dissipated through the 2.00- resistor in the circuit?

Assume the region to the right of a certain plane contains a uniform magnetic field of magnitude 1.00 mT and the field is zero in the region to the left of the plane as shown in Figure P22.71. An electron, originally traveling perpendicular to the boundary plane, passes into the region of the field. (a) Determine the time interval required for the electron to leave the field-filled region, noting that the electrons path is a semicircle. (b) Assuming the maximum depth of penetration into the field is 2.00 cm, find the kinetic energy of the electron.

Two long, parallel wires carry currents of 20.0 A and 10.0 A in opposite directions (Fig. OQ22.13). Which of the following statements is true? More than one statement may be correct. (a) In region I, the magnetic field is into the page and is never zero. (b) In region II, the field is into the page and can be zero. (c) In region III, it is possible for the field to be zero. (d) In region I, the magnetic field is out of the page and is never zero. (e) There are no points where the field is zero. Figure OQ22.13 Objective Questions 13 and 14.