Question 18.CE.3: Practice using Lenz’s law A loop in the plane of the page is......
Practice using Lenz’s law
A loop in the plane of the page is being pulled to the right at constant velocity out of a region of a uniform magnetic field \vec{B}_{\mathrm{ex}} . The field is perpendicular to the loop and points out of the paper in the region inside the rectangular dashed line (see the first figure below). Determine the direction of the induced electric current in the loop when it is halfway out of the field, as shown in the second figure below.
Sketch and translate The number of \vec{B}_{\mathrm{ex}} lines passing through the coil’s area decreases by half during the time interval from when the coil is completely in the field to when it is halfway out. Thus, the external magnetic flux through the loop’s area has decreased.
Simplify and diagram Thus, according to Lenz’s law the induced magnetic flux and induced magnetic field \vec{B}_{\mathrm{in}} should point out of the paper, as shown below, thus keeping the flux through the loop closer to the initial flux. The direction of the induced current that causes this induced magnetic field is determined using the right-hand rule for the \vec{B} field; the induced electric current through the loop is counterclockwise.
Try it yourself: Notice that the induced current in the left side of the loop is still in the external magnetic field \vec{B}_{\mathrm{ex}} (as shown in the figure above). Determine the direction of the force that the external magnetic field \vec{B}_{\mathrm{ex}} exerts on the induced current in the left side of the loop.
Answer: To the left, opposite the direction of the loop’s velocity.
